Yes both headlights can burn out at the same time, I had it happen once, it is rare. If both high and low beams are out, then I would think that it might be the switch. You could get a cheap test light and check the plug to see if there is current to the lights.
A couple of possible reasons why your headlights don't light up: 1. Both headlights are burned out. 2. The headlight switch has gone bad. 3. There is a wiring problem.
check the plug at the back of switch it may be loose
It sounds like the low beam/high beam switch is bad. Fuses are not the problem since they are built into the headlight switch and would cause headlights to blink or not come on for both high and low beam headlights.
Switch? both headlights?
To find the cause of the low beams not working, start with the bulb to make sure both are ok. Check the dimmer switch, and the wiring from the switch to the headlights.
if you've tried hitting the high/low beam switch & headlights are out on both, then a bad headlight switch or headlight switch plug or high/low beam switch plug not fully engaged.
I don't know what kind of car you have, but if the headlights work in either the dim or bright mode, but not both, I would suspect the dimmer switch. If they don't work at all, the headlight switch is probably the culpret, unless of course both bulbs are burned out, which I have seen on one occassion.
Possible that both dip beam bulbs have blown
My money would be on the switch itself... having owned a couple Gen 2 vehicles on that platform, I've had the exact same problem... running lights would work, all other lights would work, but headlights and low beams would not... it's about a $20 part, so it won't set you back much.
Possibly the multifunction switch (switch in columm). Check the bulbs, fuses etc first
could be the stalk (switch) this is a separate switch to the main beam but the whole stalk needs replacing
Bulbs burnt out? Bad hi-low beam switch? Voltage spike?