The wipers on my headlights do not operate. All wires and tubes seem to be connected to them. No fuses are blown in the box located under the hood. My automatic door and trunk locking system also does not function. Are these two systems related via the vacume system?

The headlight wipers have nothing to do with any part of the vacuum system. How are you checking to see if the wipers are working? You need two people to see if they work; one to look at them and another in the car to "operate" them.
I hope you do realize that they only come on(& do one sweep) when the headlights are on and you push the windshield washer switch.
I get alot of folks in the shop who are not aware of this, and they expect the headlight wipers to "sweep" along with the actual windshield one.

Well I'll be a monkeys uncle! No wonder I could not get them to operate. I thought they worked in conjunction with the wipers and the headlights.

Thanks a million Alain.

Smiles.