Here is an update on this little mystery. Before taking the panel off the door, I thought I would check fuses and make sure one had not blown. Turns out a little 7.5 amp fuse under the hood was bad.
The fuse was labeled “interior lights”, but it also controlled a few other things:
- The dome light
- Each of the four lights on the door themselves
- The interval speed on the windshield washer (not the slow and fast speed, just the interval speed), and finally,
- The warning buzzer that lets you know you left your headlights on.
I popped a new fuse in and at the moment, all is working fine. Of course, I realize there is a reason the fuse blew, so I will keep the eagle eye on things.