My thinking.... if it turns on and starts... for the moment your good. There are issues with the "Keyed Switches" so owners beware. (flakey cheap A$$ switches in many cases) My question in cold Colorado how did you get it started without glow plug action???
As for the other circuits best to pull the prints, study them, follow them like a road map and enjoy the journey. Not looking to be hard noised... but, they are a couple simple circuits and to guess this or that would be more confusing going on a goose chase. Owning a HumV is a learning experience. Take it to a shop and one pays for their learning time. With eye's on the road (free maps called TM's) and a mulitmeter, making the trip is easy. OK I'll lighten up on the new guy.
If factory and no wacky modifications other that your stated "Key Switch" and that seems to be OK in my guess (never say I know without MY seeing it and living it... CUZ of to many variables and SS descriptive terms. LOL
Know that the lighting circuit is it's own. Meaning it should be "HOT' at the lighting switch all the time. It does have its own internal circuit breaker, automatic resetting and nothing to see there. A good working light switch should work all of the lighting provided all the wiring / return grounds and bulbs are good. Stop and turn could be another problem.
Heater motor, wiper motor, instruments, IP, power do come from the "BOX"... Soooo having one working and not the other is a ???? or a clue. It is a bit confusing as you stated starts and runs??? When the "key' is in RUN a relay controls the IP solenoid (good as it ran) and feeds those circuits in question, another clue. (not the lighting remember, it should work any time)
New to U ? Time to "glove up" and get "eyes on" With the wiring print, TM. Lost with all those black wires? Know they have a number and hopefully the little metal numbered tag stamped near the end can be read. Could pull the dash and take a peek at the nest of wires there. Look closely at each one, to any that have pulled apart or need to be pressed / put back together or cut. There are two circuits breakers behind panel, sideways near firewall. Keep in mind that some knuckle butt may have in there before. Also... water damage. 'BOXES' have been known to fill with water, short out, crazy stuff. Another one are the couple of ground connections near the firewall, engine, all the gauges. Search here for the scoop on grounds.
Getting to know your rig is MORE that half the fun.
Find your broken bits and let the guys and gals here know. Always a story. Hope this is helpful.
Not going to guess electrical problems... don't like loosing either, CAMO
Can't help on the "BOX" thing... Don't have one.