I'm not sure where the resistor is on the rear blower. On the front blower it's mounted on the plenum box with the resistor coils in the airflow to cool them. The resistor consists of a series of open resistance windings that are switched in and out of the fan circuit to vary the motor voltage, controlling the speed. Since they get very hot from the current flow, they are not soldered but crimped together. Sometimes the crimps and corrosion get the better of them or the coils split and they open up, responding to the pounding that the OP described.
So if the resistor is anywhere near the rear motor, it should be checked before the motor is assumed to be the culprit. Locate it and fiddle with it to see if the internal connections are intermittent.
For all I know, newer models may be a different design -- electronic stuff that is not plagued by these problems. The last one I've dealt with was in a 2000, and that had conventional windings.
Here's a traditional blower resistor from a 2010 Explorer. The coils project into the plenum. See the crimps? The little semiconductor is a temperature fuse that opens if the thing overheats, as it may if airflow is obstructed.