Toyota Repair: Sienna Turn Signals w/ trailer, left turn signal, toyota factory

Question
The turn signals on my 2000 Sienna LE (w/ trailer package) work perfectly with no trailer attached.  As soon as I connect a trailer, the left turn signal flashes so faintly that you can barely see it on a dark night.  The trailer works fine with any other vehicle, so I know its the Sienna.  Can a relay work fine then stop working with only a small added load?

This may be unrelated, but when the A/C or other system kicks on or off, the headlights dim momentarily and the engine gives a slight hitch.  The dealer has replaced the altenator 4 times and ended up putting in high capacity battery and telling me it wasn't a problem.

Anything you can tell me about the turn signals, including the location of the relay if I have to change it would be greatly appreciated.

Answer
If the lights are working without the trailer hooked up there is either a problem with the trailer towing harness installed on the Sienna, especially if it's aftermarket, and not the toyota factory wire harness, or a problem with the trailer wires but since the trailer doesn't seem to have problem being hooked up to other vehicles I suspect that the trailer wiring in the Sienna is causing the problem.