1997 Dodge Caravan I can't get my parking lights to stay of

Do you think that your hazard lamps may be switched on, maybe by accident and are staying on because the seperate circuit breaker for them is bad. Try swapping the turn signal flasher with the hazard flasher. The minivans have some other problems but check and see.
Ok

The power center has a parking lamp relay, may be closed, staying closed for reasons of failure to open, or for reasons of a Body computer being told, or failing(not too often). Also if the relay control wiring shorts to ground it will turn the relay on, as if the BCM is turning it on. There are only two other very rare but possible spots. But you have replaced the turn signal combination switch with a new one, for this, right?
Yes this is always hot(12V).
Let me know. Fine group of people that run this site. You don't have a Canadian made van, do you?
They(Chrysler's engineers) ran less and less interior wiring and started with the engine power center fuses instead of fusible link wires, but the hazard lamps are usually on their own for safety reasons and were a single connector near the battery. Ok