agree with the cheese, when multiple unrelated systems start acting funny, with symptoms that suggest low voltage supply, its usually going to be caused by a bad ground connection somewhere. The logic behind this is fairly simple, the corrosion or whatever gets introduced into the ground path creates a significant voltage drop on the ground side of the electrical devices. Since the current path from battery to ground has 12v potential over the entire path, any drop on the ground side reduces the available voltage supply to the device.
I'd start by taking a static resistance measurement from the ground side of the bulbs in question to the negative battery terminal (which should be ground). That should be pretty much a short circuit of a few tenths of an ohm. If its more than that, then take a similar measurement from the negative battery terminal to a clean, unpainted part of the frame, that should also be a few tenths of an ohm. This should tell you in which part of the ground path the problem lies.
If both of those measurements check out OK, then test the supply voltage to the lights with a voltmeter. If the supply to the bulb is less than about 12v, you'll have to trace out the drop on the supply side. If the supply side voltage checks out OK, measure the voltage drop from the ground side bulb terminal to the negative battery terminal. If that's more than a few tenths of a volt then you have a ground side problem that you'll need to trace out (but the previous resistance measurements should have detected that kind of problem). Between these tests you should be able to isolate the location of the problem, then you just need to find the cause in the wiring.
