Benson, It could be a couple of things. You've covered the basics, but there are still the electronics. My best suggestion at this point is to go to the dealer and let them charge you the 60 bucks to hook it up to the machine and diagnose it. Electronic components get very expensive, very fast. As for why it takes longer... my guess is that it's an electrical short that when it gets hot, causes the malfunction. The colder it is, the longer it takes to get hot enough to malfunction. My guess is the RABS valve, but don't hold me to it. Let the dealer make the decision.
MudMan, a couple questions, and suggestions. First, if you reach down and pull up on the brake pedal, does the pedal come back up and the lights go out? Try this: Start it up in the driveway. Bend down and look at the exact pedal position. Now, press the brake by hand until it happens. Release it, and see if it returns all the way. Check to make sure it comes back up all the way. Also, look to see that the brake pedal switch is securely fastened and in position. My guess is that all is well here, since when you tunr the car off, the lights go out. Try this, start it up, and make it do it. Then, remove the vacuum hose to the brake booster and plug it with a bolt or even your thumb will work, but there's a lot of vacuum, so be prepared for the engine to rev when you remove the hose. Now see if the lights went out. If they do, then my guess is the booster is shot and is not fully releasing the pedal. If they don't go out, the master cylinder could be shot, not allowing the pedal to return, and slamming the door getting in and out is enough to free it. It's also possible that the vacuum control valve on the booster is bad, but that might be a part of the booster itself. My guess is that it's either the MC, or the booster, since it fixes tself when you shut it off.
Check it out and keep us posted.
-Joe-