This happened to me too, but it wasn't the switch.
If you push a 4wd button and the light on the switch is blinking but never goes solid, get someone to help and crawl under the truck. Have the person push buttons and listen to everything switching. You should be able to hear the transfer case AND the front axle shift actuator working.
When I did this, I heard nothing from the front axle shift actuator. $85 and about 15 minutes to replace and everything works great!
There is a youtube video from 1aauto showing how to replace these which gives us amateur mechanics a lot more confidence
I had this thing in a transmission shop for a week and they couldn't even figure out what was wrong because they believed the computer that was telling them that everything was engaging..... derp.
-2000 GMC Sierra 1500 4x4