Based on wiring diagram, it's hard to see anything other than relay.

Keyswitch fault would cause multiple On items not one.

A shorted blower power transistor should go off when keyswitch is turned off.

Only a failed-shorted relay could enable blower to run full time w/o wiring modifications.

good luck

There may be more than one problem, since it sounds like when the car is on, the blower may be working normal sometimes and not at other times.

• It may be a shorted relay for the running of the blower, et al, with ignition off.

• It may be a problem with the blower power transistor for the blower operation working periodically; e.g., when driving, etc.