4 Wheel Service light

I have a 2001 Chevy 4X4 Z71 package. The check 4 wheel drive light comes on some times. it seems to come on more often when the weather is warmer. Most of the time the 4 wheel still works but sometimes it does not. A few times the 2 wheel or 4 wheel light will not be lite up or sometimes it is not very bright.

I have taken it in for repair at transmission shops but they all say thay can not read the trouble code without the service light lite up and of course it never does when they have it.

Can you help?