First let me clarify someting you may have inadvertently wrote. The light is supposed to come on when the tailgate and/or glass hatch is opened. Hence, by your description nothing appears to be wrong at all.
All joking aside, I presume you mean that the light won't go off when you close the glass hatch. Now, in '97 there were two styles of back hatches. The first was a full hatch that pivoted at the top edge that had the glass set into it (which also opened but not when the full hatch was opened). The second was a "clamshell" type rear hatch where the back glass opened upward pivoting at the top edge and the rear gate opened downward, pivoting at the bottom. In order the get the bottom gate open, you had to open the top glass first.
If you have the full hatch, then stop reading right here. Our '95 blazer had the clamshell style.
However, if you have the "clamshell" type, then here is what to look for: With the bottom gate up and closed, look at the top center where the latch for the top glass catches and holds it closed. Just to the left of the where the top glass latch inserts into the lock is a small button style electrical switch. It is spring loaded so when the top glass hatch is open the switch is out and the light is on, and when the glass is closed the switch is pressed in by the glass and the light is off. If the switch is present, you should be able to press it in with your finger to get the light to turn off.
Three things to look for. If the switch is missing, it has fallen out of it's mounting holder and is inside the bottom tailgate. You will have to remove the inner plastic panel to retrieve the switch and remount it in it's original holder.
If the switch is present but very loose, you may be able to clip it back into position or tighten whatever fastener keeps it in place to bring it back out to it's original position. This is quite common, and the switch sinks back into the mount where it won't get pressed hard enough to turn the light off.
Lastly, the switch is OK but you have a common problem with the top glass hatch. With the top glass hatch closed, look at it from either side. If the very top of the hatch is raised above the back edge of the roof by 1/2" or more (quite noticable), then the hinges are defective and coming apart, causing the hatch to creep upward and not make contact with the switch to turn off the light. However, if the top edge of the back glass hatch is even with the back edge of the roof, then everything is fine and you just have to fix the switch only.
Good luck and hope this helps - Jonathan