Turn signal issue?

There must be a hazard flasher system. I found the switch on these diagrams, (blue arrow and circle).

First we should clarify, "constantly". We're working with two Chevy truck owners who have a single right front signal light that stays on all the time and runs the battery dead overnight. I get the impression your light only stays on constantly when you put the signal switch in the right-turn position, is that correct? If it also stays on all the time, the Passenger Junction Box is the logical suspect. That supplies the current to run the signal lights on individual circuits.

If your right signal lights simply do not flash when turned on, the better suspect would be a burned out bulb. On most other car brands, the electronic signal flasher detects insufficient current when one or more bulbs are burned out, then it still may flash the good bulbs normally, but the indicator on the dash will flash twice the normal speed to indicate there's a problem. Your model might do the indicating differently by failing to flash the side with the defect.

What I would suggest for a starting point is to turn on the four-way hazard flashers, then walk around the car and compare the flashing lights from side to side. The diagram shows just one signal light on each side on the rear, but two on each side on the front. See what the two on the left look like, then see if the same thing is happening on the right side.

If it looks like the Passenger Junction Box is defective, I can post the removal instructions for you, but it will require a trip to the dealer to have it programmed. There are multiple other systems it controls, so it's hard to say what else might not work until that programming is done.

Let me know what you find with the rest of the signal lights.