Which contacts did you clean? At the switch, the lights, or main switch connector? Or all of the above perhaps?
The dimmer is your first thing to check as the others have said. But it's not unheard of for all the filaments to be burned out at the same time either. And with a seldom driven rig, or one that's new to you, they might not even have burned out at the same time. One at a time over years of neglect can do the same thing until finally nothing works.
Another thing, once you've determined that all is well with everything else, is the tendency for old Broncos to have their radiator core supports part ways with the inner fender aprons.
Yes, even though they're spot welded together, it's not uncommon for them to become "unbonded" (electrical ground-wise) from each other. And since the grounds for the headlights are there on the core support, the circuit might no longer be able to pass enough current to light the headlights.
It can still work the lower power lights like the parking, side-marker and turn signals, but not light the main lamps.
Just a few other things to check anyway. Don't worry about the fuses at this point because the headlight switch gets it's power from the main harness and has it's own circuit breaker.
Which also means that if all else checks out good, you just might need a new switch.
One more thing that, while not all that common on EB's specifically, is common throughout the auto marquees. A burned wire at the main connector.
So if you feel like a contortionist today, pull the headlight switch and check the condition of the wires and connectors. Pay close attention to any that look like they've been exposed to excessive heat.
Oh, and speaking of wires... If this was a pre-'71, I'd also say to take a look at the firewall connectors. Finicky little buggers that they are!
But your '73 (if a true '73 and not a hybrid/franken-bronco) would not have them.
Good luck!
Paul