Wiper Motor Doesn't Work

Can we assume when it was mounted in the firewall it did have the ground strap on it ?
The motor wont run without it.
I'm not sure one can connect a 12 volt wire to any 1 terminal and get that motor to run either. They are all wired differently. For some the park switch is a player, so 2 hot wires required to get run. Good luck with it.

Absolutely true.
The multi speed motors use different windings in different combinations for the different speeds.

I think the two speed motors just use a resistor (like the heater blower does) for hi and low.