Thanks guys.
I realized today that I should check the high beams (DOH!), since the high beam light was on erroneously.
Turns out one of high beam bulbs was out. Replaced that and all my problems went away. The light stays out when it should, and the DRLs run too.
Don't know if this is an intended feature or not, or if the Contour is meant to do this, but at least on DRL-equipped cars, the car will tell you if one of the DRLs aren't working, and consequently one of your high beams are not working (by way of high beam light on when it shouldn't be). Cool.
