the mirror turn signal comes from the door switch, there are 2 harness from the door switch to the mirror. one of those wires is the turn signal, not sure which color I only know the puddle light wire is orange/black. you could just connect a meter and probe the harness with the turn signal on. connect the meter negative to any ground and use the positive wire to probe the mirror wire harness there is only about 8-10 wires per harness shouldn't be hard to figure out which one it is.
GM designed these truck's with a high speed serial lan and made each module programmable to then split the signal from each module into different functions, this was done supposedly to save on wiring. so that is why you don't have a turn signal lead going to the door, it's a digital signal from the bcm to the door switch, then it comes out analog from the door switch.
when you find the signal wire on the mirror harness that will be your positive, the ground from your led can just go anywhere on the door frame. you won't get any error messages or issue's doing this but the tech2 will pick it up as a "short to ground on the door module" it's just a heads up so you know what it is if troubleshooting something in the future