back up ligth do not work donot were are the fuss box is
I will just add, check EVERY fuse, you never know what else is blown or may be affecting something else, not just the ones you think is bad…
If it’s not the fuse, could be both bulbs are burned out.
Do not know where the fuss box is ? It is my next door neighbors 6 year old daughter.
Could not help myself. 
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Or, the park/neutral safety switch is bad, which turns on the back up lights
Tester
from what I see the PCM supplies power to the BCM for that function. From the BCM the circuit goes to the Rear Fuse Block (ref: Inside rear view mirror schematics), then via a L-GN 0.35 wire to the backup lamp. In other words, this will likely not be simple. There’s a reference to four backup lamps rather than the expected two, but the other two may be duplicates, which set you have depends on the truck’s options. If I had this problem I start by probing the voltage and ground at the lamp’s socket.
The owner’s manual probably provides a clue to which fuses may be involved, and their location.
Have trailer lights ever been wired in? If so, that’s another likely cause. My truck’s license plate lamp failed for that reason.
Until we know the 20-year-old bulbs are good I’m not replacing anything but a fuse.
George, that would make way more since if we were looking at the wiring diagram you are looking at, not all schematics are the same… Either be kinda enough to share the link to the wiring diagram or a screen shot of what you are talking about…
I have no way to do that. A screen shot wouldn’t be showing my own work and would violate Car Talks terms of service. OP will have to secure the wring diagram if they need to see it. Should be available in Chilton’s or Haynes aftermarket manuals for an 05 Trailblazer. If not, OP will need to subscribe to a service that has the wiring diagrams, or ask at a dealership.
I’d suggest OP do the simple stuff first, like what @texases mentions above.
I learned a loooong time ago never trust the wiring diagrams from either of these aftermarket manuals.
They provide false information.
Tester
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I have the Toyota factory service manual for my Corolla and also a Haynes aftermarket manual, and like you I much prefer to use the FSM wiring diagrams. The wiring diagrams in Hayes or Chilton manuals are usually direct copies from a factory service manual though, so they aren’t totally bogus. Chiltons and Haynes don’t redraw the diagrams , they just pay a fee to put a copy of the factory diagrams in their manuals. To make them affordable their manuals cover several model years and often more than one model. The main problem with the aftermarket manual wiring diagrams is the page in the manual may not apply to your cars model and year. And can be much different. Still, it is usually better to have an aftermarket diagram to reference than nothing at all.
That’s a line of B.S.
I used a Haynes manual to trace the blower circuit for the wife’s Jeep.
Not only did it omit components in the circuit, the wire colors in the manual didn’t match what was in the vehicle.
I finally went to the library to use their computer to get the right wiring diagram from All-Data.
The only good place for these manuals is on the floor, next to the toilet. In case you run out of toilet paper.
Testet
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Only in George’s world
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More nonsense ! A wrong diagram is worse than none at all .
George believes misinformation is better than no information.
Tester