96 corolla (prizm) turn signal problem-Help!

Here's a wierd one...

Turn signals and all bulbs work fine when headlights aren't turned on.

However when I turn the headlights on, the right front & rear turn lamps go on. Then the left turn signal and lamps work fine--blinking & everything. But the right turn signal does not work.

When hazards are on, the left side lights will be on, then blinks over to the right side.

The fuses all look fine.

Is this a possible relay problem? If so, which relay?

I am not the original owner, so something else may be going on...

Please help!