The 4WD light (green square light below the PRNDL lights in an auto, or down low between the speedo and tachometer in a manual) only tells you when the transfer case lever is in the 4WD position (either 4H or 4L). The "drive a bit then reverse" advice is to unlock the front hubs and turn off the "wheel lock" light (if fitted).
On the right side of the transfer case there are two switches, connected to each other with red wire. Those switches get gunked up over time and either stick on, or don't turn on at all. You can remove the switches and clean the plungers out with spray electrical contact cleaner.
When removing the switches be very gentle with the red wires, they insulation gets brittle and they can easily snap off. Also watch out for the ball bearing behind each switch, it'll want to fall out and roll away.
If the wires do break off the switch can be repaired if you're handy with a grinder and soldering iron. Grind off the top of the switch to expose the metal contacts, solder the wires back onto the contacts, and seal the top and wires with grey high-strength silicone. Like so:
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