Its suppose to go up AND down. The contacts in the rear switch are corroded or just went bad.
There are a couple different ways to tackle it. I just went thru this last fall when my switch went bad.
Here is what I had to do.
1) Remove access panel on rear gate.
2) Hook up bypass to the window safety switch on the drivers side inside the tailgate. The bypass is just a U shaped wire that goes in the connection that goes into the safety switch. not the actual switch itself, just the two wires going to it.
3) Now you can open the window with the tailgate DOWN. This really helps to have 2 people. With the tailgate down, open the window 1/2 way, and support it along the way and while your working on it. Make sure you have good supports you dont want to be buying a new rear glass
*It is much much easier to take the key switch out with the gate down as apposed to being in the up position while crawling around in the back of your blazer.
4) Once the window is in "out" position so that you can get to the nuts on the key switch, DISCO the battery. The connector going to the key switch is millimeters away from the metal framing, so if you take it off, its easy to bump metal and short it all out and blow fuses. Trust me on this, disco the battery and grounds.
5) Now there are two ways to tackle this. I dont know which is better, I can only tell you how I did it personally - I did NOT remove the regulator for the window, this makes it a bit harder to reach the 2 nuts to the key switch, but I felt I could get the nuts off without removing the regulator, I figured it was best to remove as few things as I had to. The space is extremely tight, so if you have big fat hands you will probably end up removing the window regulator. IF not than you just have to get a wrench on the two nuts that hold the rear key switch in. Once you get the nuts off, itll just fall out. You will only move the wrench less than 1/4 of a turn but eventually youll get it.
6) Now I just bought the key switch itself. I dont know what the part that the switch sits in is called but its the part that has the two studs that the nuts attach to. I replaced those studs with some nice clean ones, the old ones were rusty and the odds of getting a nut over the rusty olds would not have worked out very well. So use all new hardware and lube it up to make it easier to spin the nut on the stud, once its all in place. I actually had to have my tiny lil neighbor chick spin the nuts onto the studs as I just couldnt get it. Once she spun it on, I could get a wrench and tighten it down.
* I just remembered, I used ANTI-SEZE on the studs, ANd dont crank it down too hard, the stud will just spin in the housing if you do. The Anti-seze is in case I ever need to go thru this process again.
Over all it took less than 2hours. Be patient, this is a job you cant do quickly. I know my instructions may be confusing but once you get involved with it, youll understand and itll all come together.