the headlamp wipers ONLY work when you turn the windshield washer on.

the little motors on the wipers are prone to failure at this age and often get stuck, sometimes in the 'up' position, some get seized and sit there ticking/grinding even when the car is off.

if you look under the hood near the headlamp, a connector is there that plugs up to each headlamp wiper motor, they may be disconnected and you can try that. the replacement part is not expensive but the install is a pain in the a$$. (and in my opinion, not worth it)

my headlamp wipers have been disconnected for more than a year and even when they worked they really didn't do much but spray washer fluid on my hood. how dirty do headlamps get, really?...

good luck!
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-woodsytf '95 850 wagon 160k