1999 Dodge Caravan Blower motor

The signal to close the blower comes from your heat/ ac selector switch. If the blower "on" contacts are bad in switch, the relay won't open. Hope this helps.

If the ignition switch in the on position supplies the power to the circuits, how can the circuit be powered with the switch in the off position. The van does not have a heat/ac switch it has temperature controls, and a switch to direct air flow, push button to turn on air conditioner which operates fine in turning the air on or off and the fan motor speed which also operates fine at all speeds

Do you have auto temp control where you push buttons to raise/lower the temp?

There are slider controls for the temperature, drivers side and passenger. The problem of the blower motor being powered when ignition is off went away, and now the high beams are on all the time instead, swapped the relay for them and this did not fix. Somthing strange going on in that car. No fuses are being blown, just seems random circuits being powered when they shouldnt be??

Are the high beams on even when the HL switch is off? OR, when the HL switch is "on", you just can't dim the lights?
Does your van have "daytime running lights" DRL?