I just bought a 95 Jimmy yesterday and come to find out it had no break lights. At first the third break light wasnt even working but while wiggling the wire that goes to it, it came on. I had to tape the wires in place to keep it working. But The regular break lights still dont work. I checked the fuse, and checked the bulbs with no luck. I saw a post before about a break light switch and I thought it might be that but then the third break light shouldnt work. Any input on this is much appreciated. I know its not a blazer but from what I can tell they're almost identical.

 

Try wiggling your hazard light switch and see if the brake lights will come on. Also just check to see if your hazards are even working. It is probably linked to that switch, thats what it was on mine.

 

Another vote for the hazard switch (part of the multifunction switch in the column).

I would definitely trace down the source of that intermittent fault on the third brake light. Tapping the harness in a specific position is not a fix...