Blower motor runs all the time

Refer to a schematic. If like most blower circuits until ~2000, one wire goes to ground. The other wire is thru the switch which selects different resistors to put in series w/ the motor to control speed. The "high" position is "no resistor", which gives max current and usually so much that any connection resistance overheats and melts parts, like usually the plastic parts of the switch itself and the pneumo-push-button switch too, if your car has that. These resistors are usually in the climate air flow (to cool them, so they don't melt). You should see a plastic panel on the side of the climate box w/ electrical plug where they sit. I don't recall if removable in an old Dart. But, the resistors probably aren't the problem.

In my 1969 Dart, the blower switch was L, M, H. The "off" function was via the 5-button push switch, so that is probably your problem. Mine melted inside, which is common. When I installed a new switch (~$100 today), I added a relay so the "Hi" position turned on a relay to power the blower, taking that load off the switches so they wouldn't melt again. Same deal in my 1985 M-B, so I guess all cars were almost expected to melt stuff on "blower high", at some time after the factory warranty expired.