There are three major problems to overcome:

- the right motor

- modulated light source

- synchronization

Motor:

The easiest way would be to use a synchronous motor.
This technology was known back then, and they have been used for instrumentation.
However, they were not very common, and it's very hard to get one from that era.
I found one from the late 1930s - only one...
I ordered it for playing around with it, though, but I tend to go with induction motors that were very common in the 1920s. It will be interesting to build a synchronization system for it as well.

Getting one from that time is trivial.

Induction motors from the 1920s in working condition can be sourced from Ebay for $50-$100.

An induction motor has no brushes, and it´s very reliable.

- it is rotating at around 1700 RPM, but the speed varies with load - it´s not fully synchronous with the mains 

- when it's sped up or slowed down by force, it will change the phase, but it will catch up again to original speed

Both is important for synchronization. A common method was the "phonic motor" approach:
You mount a steel gear sprocket (or a rod in the simplest case) on the axis and two electromagnets on opposite sides.

When a synchronization pulse occurs, the coils will try to align the sprocket along the axis of the magnetic field.

When the motor is already spinning very close to the image frequency, the coils will lock its phase into place.


Light Source:

The practically usable source from that era that can be modulated fast enough is a gas discharge lamp.
Neon was the choice back then, and it was the most commonly used technology for mechanical TV.

It gets a bit harder here. There have been specialty bulbs available that had big rectangular plates, designed for mechanical television: https://www.earlytelevision.org/neon.html

But good luck finding those nowadays. I found a single one on Ebay for $300, untested, and I don't even know if the seller is genuine. 
I found out that amateurs used beehive style glow lamps like the "Osram osglim" - but I can't find any on Ebay. If you have one of those and wanna sell it, please make me an offer. Same for the big plate tubes.

There are bulbs with somehow bigger plates available, though slightly younger, 40s-60s.
Smaller bulbs are even more common - maybe using a lens or a reflector will help?
I also found a modern style "smiley face" neon bulb with big electrodes. Same stuff, might work as a modern replacement. An old part would be of course better, though.


Synchronization:

I wrapped my brain around the synchronization circuit, checked suitable vacuum tubes, but it's in an early stage for now.

First TVs of that era did not even have a synchronization signal. They just filtered the scanline frequency from the video signal to pulse the synchronization coils. This worked only if there was an image with good contrast coming in. If it was dark for a second, the whole system drifted out of phase.
I definitely want to add a proper synchronization strategy.

Detailed information: https://www.earlytelevision.org/Yanczer/motor_drive.html