Sounds eerily similar to 4-20mA controllers, only using a 0V-10V voltage to control it, vs 4mA-20mA current.

If you got one already, you can try it out with a 9V battery and 100Ω potentiometer. It’ll only reach 90% brightness, of course, but you’ll know instantly if it’ll work.

If it works, use a meter and see how much current the the bugger draws at its input pin. If the current’s small, then you can make it battery-powered. If 90% brightness is okay with you, then a 9V battery will work. Otherwise, 12V and 3 diodes in series will drop that to ~10V.

It’s not as simple as a single pot, but it’s not much more’n that.

No idea if these dimmers are built into the wall like regular on/off / dimmer switches, or if you want something external.