left rear brake turn signal interior lamp flashing?

The description sounds like either a bad ground at the left tail light module or a bad module. Being a Denali it should have the LED taillights that have a logic circuit in them which can short if water gets into the connector and corrodes. I would pull the tail light out and look at the connection. Does the reverse lamp work on that side? If yes the problem isn't as likely to be the ground as it uses the same ground. To remove the lamp, remove the two screws and pull straight back on the lamp, they can take a bit of force to remove. Then unplug the harness connector. Now see if the issue has gone away, if it has it's most likely another module failure. Just be setting down when you price the replacement module.

Yes, the reversing lights and park lights work; only the brake lights and turn signals don't work, and the dome lights flash at the same time as the turn signals.

Yeah that sounds like the wiring isn't the issue but the light module itself, not uncommon unfortunately. Not sure who thought it was a good idea to put control chips in the tail lights.