Do your exterior lights (running, tail, side markers) still work? Blowing the exterior fuse can take out your dash lights as well, since those are fed off a branch of the exterior circuit (although they do have their own fuse as well).
replaced the headlight control (twice) with no resolution of the problem
You mean you pulled the headlight switch and replaced it twice? Were you installing a new one or used one each time? Your symptoms indicate that the dash lighting rheostat in the headlight switch has flaked out on you.
Check which wires at the headlight switch connector are hot. Then see which ones go hot when you pull the switch out to first position. The brown wire is exterior lighting, and...
Pause while Andy goes rummaging around the service manual...
Ah, here we are. For the '93 and most similar years, here'* the scoop:
The brown wire coming out of the headlight switch is your exterior lighting circuit (except for headlamps, which are separate). Aside from going to your taillights and such, it also runs a brown wire down to fuse 21 on your instrument panel fuse block, which is your dash lighting circuit, a 10-amp fuse. On the other side of that fuse, a dark green wire goes back up to the rheostat in your headlight switch (through the same connector as the brown wire, in fact: C2). Variable power comes out of the rheostat on the gray wire (via the other connector: C1) and is distributed to your dashboard backlighting.
1) See if you've got power coming out on the brown wire when you turn on the parking lights (if your exterior lights work, you must have)
2) See if fuse 21 under the dash is good, and has power on one of its contacts when your lights are on
3) See if the dark green wire going into the headlight switch is hot when your lights are on (this may be kind of tricky to test, since you must have the headlight switch plugged in and turned on in order to verify this)
4) See if the gray wire coming out of the headlight switch has any voltage in it when the **** is pulled out. Try slowly turning the **** as you test this.
Let us know what happens...