Why won't the automatic headlights and ignition chime shut off on a 90 Mercury Sable?

Turn the manual switch to "off" for the headlights to kill the lights, and it will quiet the headlight warning chime.

Another solution would be to check the operation of the plunger switches in the door jambs. They have a single (positive) wire connection, with a plastic insulator that dry-rots, allowing power to go to ground. There are also switches connected to the door latches, if the latch doesn't close, the circuit remains open. I use Electronic parts cleaner to remove old grease and grime, and then use white lithium or HD silicone. Check the post on the door jamb (where the latch engages). It's supposed to have a plastic (delrin) spacer on the metal post. If it's broken, missing, or the latch has cut through it, the door won't close tightly. Leading to water leaks in the rain (or carwash), an annoying rattle, and high-pitched air leaks at highway speeds. No easy way to replace it, the post has to come out. Make sure your Torx bits are Chrome-molybdenum or titanium and covered by a warranty, get out the big breaker bar. A TEMPORARY fix is to wrap the post in layers of electrical tape. The latch WILL cut through the tape and the door will rattle again...