Four wheel drive not working?

Being a 1999 it should be a shift on the fly, not shifted while setting still. The system works in 2 high and 4 high by just selecting either one while at a speed up to around 45 mph or so. To get into 4 low you first shift into 4 high, then stop and shift the transmission to neutral and then the transfer case into 4 low.
From your description it sounds like the transfer case may be stuck in neutral. I would try shifting it through the various settings on the switch a few times with the key on but engine off while listening to see if the transfer case is actually shifting and if the lights change as well. If the truck is a normally driven 4 wheel drive it's possible that it has only been shifted into 4 wheel a handful of times and has corrosion in the motor and selector under the truck which is causing it to stick. By switching it a bunch of times it might free up.
The other option would be to remove the transfer case shift motor and test it with it off, but if it frees up on it's own it saves a lot of work.
To remove the shift motor you need to get the truck high enough to get under it. Then you unplug the transfer case motor and remove the lower brown wire from the motor side of the harness, it attaches to the truck harness so if you don't de-pin it you cannot remove the shift actuator. Next remove the bolts that hold it to the transfer case starting with the wiring harness retainer. Then the rear bolt and then the front one. Then the motor pulls off of the shaft. There is a triangular shaft that shifts the internal parts of the transfer case, note it's position before you try to install a replacement unit, you may need to rotate it using some pliers to get the new unit on.