These same style motors are used in a host of small appliances including hand held battery vacuum cleaners (dust busters) and slot cars.
The trick is to get a motor that spins at the same RPM as the original.

The motors burn out usually because of a vacuum leak somewhere in the door or HVAC controls. If there is no leak the system becomes vacuum "charged" and the motor stops operating. If there is a continuous soak of vacuum the motor operates continuously. There is a detector in the pump that shuts off the electric motor when enough vacuum is "stored" in the system.

Wheh replacing a faulty pump or repairing the motor makes sure you get a vacuum tester and find where the leak in the system is. - usually the HVAC flap rubbers gone bad, perished or broken.