had a very similar problem on a 2001. i tried one of those aftermarket led bulbs ro brake/tail/signal on the back, and they never lit up, so i went back to the original bulbs and they worked, as the first thing i did to test them was put on the flashers. everything was fine untill i turned the headlites on, poof, dark. started checking all the fuses, cb;s, etc, and no blown fuses, in the dask box, or the under hood fuse box, that had anything to do with lites. so i started wth the upper right fuse and worked my way down each fuse untill i found a 10 anp fuse blown. checked the map on the underside of the box lid and it had initials TRLLTL, close any way, anyhoo, replaced it and poof, all lites work in all conditions, etc, back to normal, so i call a gm mechanic at the dealership i bought it from new and he said that the fuse was pre-installed for trailer light, incase someone ordered a trailerhitch, the dealer ship istal's them and just plugs into the harness, but he couldn't figure out why that fuse blew the tail lights out using flashers and headlites.
good luck, and good hunting.
excheezhead.