I'd say something is wired wrong - the rear turn lights are actually the brake lights, and having the headlights on should have no effect on them - unless somethings shorted somewhere
the circuit is: power [orange wire from S on light sw] to the brake switch, then to the turn sig sw assy, then on to the rear brake light, one wire to each light assy ... the tail lights [black wire] get power from the T terminal on light sw, and that wire is common to both lights
when you signal, the seperate power from the signal assy is sent to the relevent rear light brake element - if you are applying the brakes at the same time, the flasher interrupts the power applied from the pedal sw ... make sure you have
the connectors underneath hooked up correctly [info for Chevy, but I'd expect to find the same on GMC] - if you have aftermarket rather than factory signals, should have a similar routing setup
Bill
