The main thing is your 4 wheel drive works just fine I have a 3 button switch also, I have a 98 LT 4x4... If it were me, I would buy a new switch and see if that does the trick... In the States the 3 button switch is like $30 bucks or so but in Poland I have no clue

 

Guys, please...
If there's a non-working button, it won't switch over.
If the button back light is dead, then it won't blink.
I have the feeling it could be a missing feedback signal from a change-over detector at a transfer case. But I don't have the right wiring diagram,

 

Here's the 3-button transfer case description, diagnostics, and wiring diagrams for a 2001. Should be the same for a 2000 3-button ZR2.

https://blazerforum.com/forum/2nd-ge...-blazer-89670/

 

Hmm, from the schematics its either the:
- encoder set that reads the position or (more likely)
- it is calculated from a VSS sensor (less likely)

 

I have another switch but car is still at the mechanics. They need to do some other things.