between all of the blazers I have had, every light related problem has been a ground. On our blazers the ground goes right onto a screw behind the light assembly. I have also seen some with grounds that clip/slide into place.
check at you engin harness, the tailights have a harness that will come from under the drivers side of the cab and plug into it, there are 4 wires if I remember right, some times for some reason or another the wires can get pulled, streched or the conection into the harness could ust plain be loose.
go to auto zone and get a battery cleaner brush tool, insert that into the socket to see if you can clean it up some, could be corroded like the above person said.
get a cheap tester light too to help you hunt it down, also have you messed with your exaust? poor routing can burn the wiring, the past owner of my 86 had the muffler put real close to the frame, it killed my wiring to my rear light,
good luck, the wiring on these trucks is not that bad, but it can still make you nutty.
-shawn