This is quite simple but may at first be confusing for MGA owners and mechanics. Notice the picture of the back end of the vacuum regulated turn signal switch for the MGA (and some other cars of the era). The terminal designations molded into the housing are "F", "L", and "R".
For the MGA 1500 the "F" can mean Flasher. For the MGA 1600 the "F" can mean Fuse. This is the power input terminal for the switch. The "L" and "R" terminals would seem to be labeled for Left and Right turn signals, but for the MGA this is backward, where "L" is connected to operate the Right turn signal and "R" is connected to operate the Left turn signal.
This seemingly odd terminal labeling likely originated with an earlier application where the manual input knob, shaped like a single wing, was installed with the wing oriented upward from the shaft. Then when you push it toward the left the shaft would rotate anti-clockwise, and toward the right would rotate clockwise. That is the direction of rotation required for these terminal designations to make sense.
As this switch is installed in the MGA, the wing on the knob hangs downward. Pushing it to the left makes the shaft rotate clockwise, and to the right rotates anti-clockwise. This means you have to hook up the Left turn signal wire to the "R" terminal, and the Right turn signal wire to the "L" terminal. If your MGA turn signals seem to work backward, this is likely the problem and the fix. When in doubt, use a test light or ohm meter to check continuity for the switch terminals when you operate the input knob. Also pay attention to the color coding on the wires.