Can I bypass multifunction dimmer switch and get headlights to work?

Your year--make--model didn't post for some reason? That info would be helpful.
If your dimmer switch is part of multifunction switch, I'd have to check multifunction switch and wiring circuits.

Things to check; common wire for ground may be disconnected so take the common wire and run a jumper to the battery.
lights could be bad they wear out too. Substitute
a known good lamp in both sides to see if this fixes problem.
Headlights also go thru the dimmer switch so run headlights to battery with a jumper wire. This bypasses headlamp switch and dimmer.
Consult the owners manual for fuses,relays and their locations. One fuse box is usually inside passenger compartment and another under the hood.
Hope this helps.

your switch is not good try to double check your switch.

When you had the wiring loose for multifunction switch, if possible, knowing what color wire did what, using wiring diagram, I believe you could have used jumper wire to bypass multifunction switch to see if this or that system would work, if it doesn't, the multifunction switch probably wasn't the problem. On older vehicles it was probably easier to do something like that. Could be issue with wiring in steering column or clock spring, where applicable.Your low beam from dimmer switch goes through drl relay, with relay not energized. At the low beam head lamp, tan wire is voltage, black wire is ground.

You need to check the wires in the steering column. Take the column cover off, probably phillips-head screws, so you can see the wires. Somewhere the tilting function is putting pressure on the wires to the dimmer switch. It may be pulling loose a connection, just a fraction, to lose contact. You may also need a new dimmer switch. Or a multifunction switch if the dimmer switch is attached that way. The headlight switch is on the dash, isn't it? If it is, the headlight switch is not the problem, it is the wires in the steering column or the dimmer switch. If the dimmer switch fails, you will have no high or low beams, no head lights at all.

I don't believe there is a fuse. There is a circuit breaker built into the headlight switch. If you are sure the headlight switch is good, it could be a bad dimmer switch. If you have a voltmeter, with the headlight switch turned on, a larger yellow wire going from the headlight switch to the dimmer switch should be a hot wire. The dimmer switch sends power on a tan wire to the low beams, and through a light green wire to the high beam bulbs.
If your high beam indicator on the dash also doesn't work, then it is likely one of those switches. A voltmeter or test light would need to be used to find which one is bad. If you can find the connector at the steering column going to the dimmer switch, pull it apart and check for power on the yellow wire coming from the headlight switch, with the headlight switch turned on. If no power, the headlight switch is bad. If there is power there, then the dimmer switch must be bad.

The headlight switch gets power for the headlights from a 50amp fuse.
The fuse powers the headlight switch then the dimmer switch breaks for high and low beams. So if the high beams work, the problem may be with the dimmer switch.
The dimmer switch is made into the turn signal switch on the column. You would need to check the low and high beam circuits at the switch for power.

The power goes thru the fuse, then thru the headlight switch, then the dimmer switch. If you don't have power at the fuse you may need a shop manual to get the wiring diagrams to trace the circuit back to the battery. Its supposed to be hot all the time.

All go out at once, first check fuses,then dimmer switch for dash lights, finally headlight switch. To check dimmer switch, pull connection off back, on harness with test light and headlight switch activated, 1 of the leads should have power, if so, use ohm meter on dimmer to make sure it has reading between 0 and some value, if no value, open, dimmer is bad, if there wasn't power then check headlight switch, there should be heavier gauge wire that powers switch and 1 for output to hi/lo switch, smaller gauge wires for tail lamps, dash lights, license plate lamps, parking lights. The color wires from dimmer would correspond to the same colored wires on headlamp switch, probe that connection on headlamp switch with switch engaged and see if you have power, if not replace switch, if so, check wire from switch to dimmer.Now if the lights slowly went from bright one day, to less bright some other day, to not working, then the bulbs are bad... good luck...

The proposed problem sounds like the problem I had with a 95 Mustang. Check the tail lights as well as the dash lights. If both are out when the headlights are switched on, the problem more than likely is with the headlight switch. The 95 had a poorly designed wire and plug configuration going into the switch. The wiring was too small and the plug would literally melt. The headlight switch and plug has to be replaced in this case. The problem was supposed to have been cleared with the 96 Mustang; however, a persistent problem may suggest checking the plug/switch combination.