Alright, I’ve finally gotten around looking into this more. With spring around the corner, I’m going to need those windows down!
When I hooked up the motors directly to the battery, the old motors worked fine.
Using the voltmeter, with one probe on a lead and the other probe grounded to the door, I got 12V. When activating the switch, 12V went to 0V. With both probes on the leads, the meter read 0V-- which makes sense if they both independently have 12V, right?
However, when I pressed down on the switch, the voltmeter continued to display 0V. (Similarly, when I poked the voltmeter probes directly into the wires near the switch, I got 12V, similar to the leads at the end of the wires.)
Seems to me that all the wiring is fine all the way up to the terminals that connect to the window motors. However, it seems that there must be some malfunction in the switch’s function to replace one of the 12V to ground when activated (see Koan’s note) seeing as how activating the switch did not cause 12V to go to 0V.
I noticed in the manual that there are 2 types of switches, and that “the 1 terminal has 2 alternate positions” :

Do these 2 positions vary according to the left and right side switches? The 2 switches I have are identical.
Is it possible that I have 2 right side switches, and that this could explain all of my problems? (When my windows first went out, I immediately suspected the switches, and ordered a new driver’s side switch, but perhaps it wasn’t actually a driver’s side switch this whole time…).
Could simply getting a proper driver side double switch solve my problems? If so, where's a good place to order one online?
Thanks!