"I'm having some trouble figuring out why my turn signals don't flash. Is there a way to test the flasher unit before fiddling with other things? And just out of curiosity, how does the flasher unit work?"
The flasher unit is the metal can shown in the picture on the right. Click for larger picture (and yes I know there's a wire loose). It has three screw terminals, "B" for Battery, "L" for Load, and "P" for Panel (dash indicator lamp). If the terminals are not marked you can check it with a test light or ohm meter. The "P" terminal will be open circuit at rest, and the other two terminals are functionally interchangeable. The canister does not need to be grounded, but it does need to have the correct electrical load to operate properly. And yes, you can test it by itself, but you do need to use the correct electrical load for the test.
The flasher only works properly when it is driving two 21 watt lamps in parallel (for the turn signals of course). This 42 watts is a load circuit with (nominally) 3.43 ohms resistance (6.86 ohms for each operating bulb with hot filament). If you want to use a resistor to emulate the electrical load for testing, you will need a 25 watt power resistor with any resistance value within about 10% of 3.43 ohms (within the range of 3.1 to 3.8 ohms). The 25 watt resistor is large enough, because the operation of the flasher is only about 50% duty cycle for the load. If you don't have the (expensive) power resistor handy, and don't want to buy one, you can hook up a pair of 21 watt bulbs in parallel, either in lamp sockets or by soldering wires to the bulb contacts. Or if you have enough confidence in your car's wiring integrity, you can just connect any two of the 21 watt bulbs in the car.
To test the flasher unit, do the following:
a.) Connect a hot wire (12 volts) to the "B" terminal of the flasher unit. In the car you might just switch on the ignition and use a test light to verify that power is connected to the flasher in the car. If you expect to do more than a few minutes of testing in the car, you should disconnect the ignition coil to avoid overheating and possibly damaging it.
b.) Connect the load (resistor or lamps) between the "L" terminal and ground (return to the earth terminal of the power supply or battery). In the car you can use any handy ground point on the car.
c.) Connect a grounded test lamp to the "P" terminal on the flasher unit.
With power and load connected, the flasher unit should commence clicking loudly on/off about one cycle per second (as you would want the turn signals to flash). If you have lamps connected for the load, the lamps should flash, and the lamps will get hot with about 10.5 watts of heat each at 50% on/off duty cycle. Using a resistor for load, the resistor will start to get hot with about 21 watts of heat (at 50% duty cycle of the flasher unit). The test lamp should also flash on/off in unison with the clicking. If it clicks at about the right rate, and the test lamp also flashes, then the flasher unit is in good operating condition. It does not hurt the flasher unit to leave it connected and operating for an extended period of time.
If the flasher unit doesn't click at the right rate, or the pilot lamp doesn't flash, then the unit is considered trash and needs replacement, because it's a sealed unit and generally non-repairable. If you were the curious type you could pry it open to see what's inside (nothing to lose but your time). For a non-working pilot lamp you might be able to clean the contacts. For a non-clicking unit you might have to rewind the heater element wire, which is beyond the scope of these test instructions, and also probably not cost effective.
End of test. Beyond that, if you understand how the flasher unit works, you may better understand some of the flasher quirks you may encounter from time in your car, and might be better equipped to repair the other problems.
Inside the flasher unit is a bimetal strip that will bend when heated. It is mounted in such a manner as to snap suddenly (and loudly) over center when heated or allowed to cool. This sudden change of position makes or breaks a relay contact to cause the turn signal lamps to flash. There is a winding of heater wire wrapped around that bimetal strip. One end is connected to the system power terminal "B", and the other end is connected to the output terminal "L" (going to the load). Passing a small current (less than one amp) through this heater wire causes it to heat up (about 7 watts of heat) and in turn heat the bimetal strip to make it bend and snap into the alternating position. Otherwise the thing looks like a single throw relay with a normally open contact, with the armature being operated by heat rather than a magnetic coil. When the flasher unit heats up and switches, the contactor shorts the input terminal to output terminal, which kills the voltage that was driving the heater. Then the bimetal strip cools off, and the contact snaps back open, and the cycle starts over again. Current will not flow to operate the heater element without the proper load connected to the output terminal.
To further understand how the whole flasher system works electrically, you need Ohms law and a simple power equation, like this:
E=IR (voltage = current times resistance)
P=(I^2)xR (Power = current squared times resistance)
By algebraically manipulating these equations you can represent and solve the electrical conditions in the flasher system.
When you put a voltmeter on the "unconnected" output of the flasher unit you will see 12 volts, but only because it's open circuit. If you touch it with a grounded test lamp, the lamp will light up, but not quite at full intensity. The resistance of the internal heater element is about 12 ohms. The resistance of a 3 watt test lamp is about 48 ohms. When connected in series this gives about 9.6 volts to drive the test light, which why it is not at full intensity, and you may read only about 2.4 volts at the flasher output terminal. Total circuit resistance is 60 ohms, so current flow is 0.2 amps. This generates about 0.5 watt of heat in the flasher, which is not sufficient to make it switch.
When you connect two 21 watt turn signal bulbs in parallel, and connect those to the flasher unit, the external load resistance is only 3.4 ohms. In series with the heater in the flasher that makes 15.4 ohms total circuit resistance, which will allow current flow of 0.8 amp, which will generate 7.3 watts of heat in the heater element. At the same time each of the two light bulbs gets 0.4 amp and 1.1 watt of power at about 2.4 volts. This is insufficient to make the bulbs light up, but the bulbs are the necessary ground return path for the heater element in the flasher unit.
This is the proper amount of current and heat to make the bimetal strip bend and switch over center. When the flasher switches like this it connects the flasher input terminal to the output terminal (and also to the pilot terminal). This applies the full 12 volts to the load to make the lamps light up. At the same time the heater element loses all drive voltage because both ends of the heater wire are then connected together by the switch (shorted). With no heat supplied, the bimetal strip then cools down until it relaxes and snaps back to the original rest position, opening the switch contact and killing the lamps. This also breaks the short across the heater element, and with power restored to the heater the cycle starts over and repeats, at about one flash per second.
As a matter of some interest, it may be noted that there will be a short delay of about 1/2 second between the time power is first applied and when the turn signal lamps first light up. In the MGA 1500 car with the turn signal relay box, the first click you hear when the turn signal switch is activated will be the relay switching on, not the flasher unit.
Although the flasher units have been known to last for decades, the eventual failure mode will most likely be a broken wire in the heater element. Before that happens it may develop a corroded contact for the pilot lamp, thereby disabling the indicator light on the dash while the turn signals still work. The next failure mode is very unlikely because the wiping contacts are generally self cleaning, but if the primary load contacts were badly corroded the flasher would switch to the actuated position and stay there as long as the power is on, as the contact would not be made to short our the heater power (and no power for the turn signal lamps).
If you add a third 21 watt bulb (in parallel) to the load there will be about 1.1 ohm less total resistance in circuit (7% less resistance), the flasher will see a bit more working current (8% more current), the heater element will heat up faster (about 16% more heat), it will attain slightly higher temperature and will take longer to cool down (nearly double the time) before it switches back. This makes for an overall slower flasher rate with quite a bit more "on" time and just a tiny bit less "off" time. Total cycle time is then about 50% longer, or about 1.5 seconds per cycle. That's not bad, because it tells me my trailer turn signal lamp is working when it flashes slower.
But if one of the car's two turn signal lamps is burned out or not properly connected, then the flasher unit sees double the external resistance (only one lamp connected), and it probably won't flash at all (about 33% less heat in the flasher heater element). When it doesn't switch, the turn signal lamps will never light up, because the rest position of the flasher is open circuit. Not flashing is the indication that there's something wrong with your wiring, or that you have a burned out bulb, and no operating turn signal on that side of the car.
Additionally, the MGA 1500 circuitry has the turn signals sharing the rear bulbs with the brake lights. That peculiarity (and associated quirks and problems)is discussed in the next lesson on the 1500 turn signal relay operation and fault diagnosis.