I still have these questions though...
What is a non-PWM motor called? (is there such a thing?)
Is it trivial to wire a non-PWM motor?
Would a multimeter react fast enough to determine if the controller is using PWM?
I don't really think that there is much difference between a PWM and non-PWM motor, for permanent magnet DC motors with brushes. I would guess that there are some differences, but lots of motor are run with PWM without specifically being designed for it.
Yes, it is trivial to wire a non-PWM motor. Connect it to a power supply. For example, look at stove fans. They have a DC motor wired to a Peltier element. The Peltier element generates electricity and the motor turns. That's it. There is no control device, no switch or anything.
In the more normal case where there is supply that is switched on and off to make the motor run or stop, there will be a larger current when the motor is stationary, so some consideration of the starting current need to be made.
A multimeter on DC will never react fast enough to determine if the controller is using PWM. However, better multimeters will measure the AC component of a voltage, and ignore the DC component if the multimeter is set to AC. To test that, select AC on the multimeter and see if it reads anything when connected to a battery. If it reads zero, then you can use it to see if there is an AC component on the voltage from the controller to the motor.
It's not a perfect measure, as PWM will be in the range 1000 - 50000 Hz and multimeters are sometimes only made to read AC voltages for mains at 50 - 60 Hz.
Almost all speed controllers for DC motors are PWM.