I'd check the resistor pack.  Except for high speed, all the other
speeds send the power thru the resistor pack. It should be located on
the side of the ductwork somewhere with four or so wires plugged into
it.

Well, we'd first need to know which "flavour" of climate control system you
have.... would this be the manual climate control set up or perhaps the dual
range electronic climate control?

I am totally ignorant as to what a "post full of mechanics" is but I imagine
a military base where a lot of guys have tools..... Sadly, owning tools
doesn't assure knowledge - especially when we are discussing what might be a
pretty sophisticated system.

<My question is now, how do I know for sure and how do I fix it?> This can
be complex... For these types of concerns (and I have been doing this stuff
for enough years that the military will NOT want me hanging around waiting
for my heart attack) I refer to the workshop manuals and the wiring
diagrams. I identify the system I am working on and I proceed with a logical
diagnostic progression.... Knowing "for sure" is going to entail some
"testing" using "tools".....

Flesh out your post with some pertinent data, let us know if you have a DMM
and give us some idea of your abilities.... If it was as simple as you seem
to think, I'd be out of a job.....