The headlight pops up with the stripped gears bc of the way it works. They stop turning the pop up motor when it senses a high amp draw, then the circuit shuts off. When the gear strips, there is no high amp draw as there is when the ger hits the stop, the motor keeps turning, and the circuit remembers this. It is a default setting so at least when the gear does strip, the headlights will still come up.
Most likely you don't need a harness, it is a dual filament bulb. Does the turn signal flash on that RF the same intensity as the LF? An easy check is to put on the hazards and look at them. Sounds to me like you have a bad light/socket.
Nah, they are still cool no matter what.
True, but we really don't have much fog in the states, compared to Europe. These lights are mostly for style, and I think they nailed it on Trans Ams!
The few times I've been in thick fog, tho, they have helped. I won't soon forget the stress of driving I-65 South to New Orleans, the first hour was all fog. Try driving like that at 50 MPH, can't see anything but have to trust the taillights 3-4 car lengths ahead of you that you barely see!

