Thanks Rockledge, you've been helpful as usual. You were right, it was a bad relay.
For anyone like me who had no idea where to look, here are some pictures. The relay box is located to the right of the steering column and is sorta attached to the side of the console housing the A/C controls, stereo head unit, etc. Here is what the box looks like with the cover on:
Here it is with the cover off. Mine had electrical tape wrapped around it twice so it was a little hard to remove.
There are 5 relays in the box. I believe the blue one is the turn signal relay. The larger black relay below that, I'm not sure about. The three below that are all identical (marked with F57B-14B192-AA) If I remember correctly, the one that fixed the light problem was the one on the left, second from the bottom. But it was possible that it was the one on the right. I pulled a few relays from a 2000 Explorer at the local pull-your-own place and got them for $2 a piece not realizing until I got home that the smaller ones were interchangeable. But anyway, it's fixed and it wasn't major surgery to do. Didn't even have to remove a single screw.
Once again the FTE forum saves the day (and a lot of money).
