While I do not have a diagram, I would think that the wire you describe as "hot all the time" should likely be tied to ground, perhaps there was a star washer/wire loop under the switch where it pokes through the dash. Especially if the wire is a black wire.
The question is if it remains hot with the key switch off. If the key switch shuts off power to it, there should not be any problem, but check where that hunk of wiring harness leads to just to make sure it doesn't fail out in the field. Just check the things that share that hunk of harness (lights, fan, etc.)
Any time an item in circuit is getting a voltage, as an example- say you remove the only ground from the headlights, with that headlight switch "on", you will not have lights but you have 12 volts (or 6 volts on a 6 volt system) between ground and the head light ground wire you removed from ground- the test light or meter is completing the circuit to ground, but the internal resistance of the meter, or bulb is limiting how much current is flowing the circuit, which in most cases is not enough to allow anything to operate.