Ok, so I took some pics to go along with my write up. First of all a nice pic of the inside of a military tail light housing.......As you can see there are 4 bulbs(this is a newer housing so it has some led stuff, the older ones would have actual bulbs like the top. In order from the top are: running light, just lights up the lens at night, second: Brake/turn signal, third and fourth have to do with the black out settings so we aren't going to deal with those here.
Second pic is a close up of the top of the housing, as you can see there are the 2 wires in the foreground that go through the insulators, those 2 are the ones that bring positive power to the 2 bulbs, the one on the left goes to the brake/turn bulb, the one on the right go to the running bulb. The other wires in there are the ground wires, just under the brake bulb is riveted to the metal and goes to the right post on the back of the housing(which is where the rear mounting bolt goes, the left wire goes and does the same for the bottom 2(black out) bulbs and hooks to the left rear post, again the mounting bolt goes there.
As you can see in the 3rd and 4th pics the bulbs in question.......both are brake bulbs, the one on the left is a civilian 12 volt that is in almost every car on the road(until newer ones that use a flat blade instead of a metal socket), the one on the right is the bulb from this housing. You can see both are double filaments, however the left one has 2 wire contact point on the bottom and the one on the right has only one. In the left bulb the small filament is for the running light and the large filament is the brake, 1 bulb 2 jobs......in our bulbs there is ONLY 1 contact so BOTH filaments do the same thing....remember the top bulb it does the second job of running lights..........
Now as the same way every GM car is wired the brake light and turn signal use the same wire, If you are on the brakes the bulb is lit and when you use the turn signal it starts to blink, NOT brighter, just blinks.....so the other side is the only light that says light with the brakes........the exact same thing is with our military trucks, Everyone gets hung up on the 2 filament thing, but it doesn't make any difference!! it is still just 1 bulb, 1 job just uses 2 filaments to do it.
Now if you are still with me.......as to the problem you are having, it can ONLY be one of two things....IF the lights were operational as intended BEFORE you changed them out: 1 IF you crossed 2 wires, then the wrong bulb will light(very hard to see if it is one of the black out bulbs.....so take off the lens and watch as someone presses the brake........IF NO bulbs are lighting with the brake pressed then it is problem 2, BAD ground or bad bulb.......easy to track, put in the bulb from the original light that you KNOW worked, if nothing then ground!!!! easy as pie.
Edited: helps to actually attach the pictures