Guys, I've got a turn signal problem that I haven't been able to sort out. I'll do my best to lay out the symptoms below. Any help is greatly appreciated!!!

When the headlights are off:
The front left and right turn signals function correctly.
Both rear turn signals flash at the same time when the turn signal switch is switched either direction.

When the headlights are on:
The front left and right turn signals and side markers are both on solid (all the time, regardless of turn signal switch position).
The taillights come on, but the turn signals don't work. The side marker lights don't work either.

Again, thanks in advance for your help!

Do the brake lights work, with and without headlights???

Poor grounds, either at the sockets or at the ground wires. Turn signals and parking/tail lights are 2 diff circuits that share grounds. Turn signals work without headlights/parking lights on because they are grounding through the parking/tail lights. When you turn on headlights/parking lights, the ground is lost for the turn signals.