Many Hvac blower motors, dont use ball bearings, just a oiled bushing surrounded by felt. They can and do draw more amperage when this lube is dried out, and the lower the voltage is, the more amperage the already undersized wire and ancient oxidized connections are trying to carry, causing more voltage drop and less voltage reaching the struggling motor.
I cleaned my carboned up speed switch's contacts, more than once, before replaced burnt portions of its harness, and the motor itself, and its resistor, and thickened up all its wiring which solved the issues.
What I should have done earlier, was just wire the motor directly to a PWM motor speed controller, as all those circuit upgrades are now bypassed in favor of the latter. I now have infinitely variable fan speed, that also wastes less alternator/battery power by heating the speed reducing resistors.
I also enjoy being able to power the fan with engine off, no key in the ignition, even with the possibility of human error induced battery depletion.
Here is one example of such a product.
Rated current: 40A Maximum output current. - PWM Regulation range:5-100%. - It is fit all kinds of general-purpose and have a DC motor speed with brush. - PWN Frequency : 200hz.
www.ebay.com
Note that below 21khz they can make the motor make an audible whine to human ears at reduced speeds.
Lubing the felts of the Hvac motor might be worthwhile. The VW Vanagon guys who have to rip apart the entire dash to access the motor, drill a port in the housing in order to be able to add oil as the felt dries up so they don't have to rip apart the whole dash each time.
My replacement VDO branded blower motor has has issues with the brushes sticking, remedied the second time by reducing their size with 800 grit.
I have hundreds of hours on this motor with the 40 amp/ 60 amp surge PWM speed controller. My Motor will draw 12 to 18 amps at highest speeds, depending on system voltage and the position of the diverting doors which place more or less resistance to the motor.
I have extended the potentiometer wiring for the On/OFF combined speed dial and mounted it next to the original 4 position lever speed switch. I can swap 2 anderson powerpole connectors and return the rebuilt original blower motor circuit to full Function, but there is No reason to do so, and i regret the efforts I expended to do so, before I went with the PWM motor speed controller.
If you are not concerned about the original switch's function, then the PWM motor speed controller can be the easiest cheapest , and permanent solution, and yield more function, more efficiently.