the problem is the switches themselves, just poorly designed.
If the high beam switch is broken that it should be replaced. When the unit is replaced the high beams will work again.
Normally caused by faulty dimmer switch.
Have you checked the daytime running light module?
It might be the high/low beam switch. Had to replace one on my '96 when I had only low beams.
I have a 98 sunfire gt and i have only high beams which only switch on sometimes and no low beams just day lights my shop told me it could be wiring or turn signal switch they looked and determined it was the switch so i just ordered it. They can be found on carpartwholesale.com or autopartwarehouse.com for only 30 or 70 with cruise control. only need a torx wrench and small screwdriver to replace it just snaps into the wiring harness.
headlight switch
You might have a bad high/low beam switch. If it's the stalk type like the Sunfire's have, meaning it shares duty with turn signals and cruise control, a replacement is not overly expensive and is a do it yourself job. A Haynes or Chilton manual will walk you through the job.
The contacts in the dimmer switch, on the steering column, may be burned from the headlamps being on all the time. The switch has to be replaced. First check the low beam lamp filaments with an ohm/multimeter for continuity.
Pulling the turn signal switch toward you should switch the lights to the low beams. If that doesn't work, you may have to replace the switch, which means replacing the entire turn signal stalk.
check multifunction switch, modules & relays
Low beam bulb burnt out? Replace bulb. Bulbs OK? If the dimmer switch is also the turn signal/cruise/headlight on and off switch, you probably have to replace the entire switch.
a loose wire or a broken switch inside the cab