No air or heat but everything works

Well, I am completely baffled. On Sunday, the blower motor in my Mini decided to stop blowing air on all settings. No heat, no A/C, no nothing. So tonight I went through the hassle of pulling the blower motor out (worst job I have ever had to perform. It is not under the dash, it is behind it. I cried. Not joking.) And testing all the components individually.

I tested the blower regulator with a multi-meter, and the voltage continuously stepped up with each setting, topping out at 12 volts on the highest setting. I unplugged the harness from the back of the blower motor and tested that as well. Same reading, 12 volts. So then I started the four hour task of pulling the motor out (did I mention how much that sucks?), And would you not know it, it spins just fine when applying voltage to it externally.

I am stuck. I have no idea what could be wrong. If there is 12 volts coming from the harness into the motor, why would it not spin like it does when I apply 12 volts to it with a charger? How does that make any sense? Am I missing something? I have come to terms with the fact that I will have to spend money on parts, but nothing appears to be broken!