Due to some forum post on CN I had a look at the joystick driver for INDI, and connected a gamepad to my mount computer.
It was properly detected, and I could enable joystick support for my mount (ieqlegacy).

Testing it I first thought it doesn't work, but then heard a very faint sound. It was moving, but very slow. So I checked the mount control panel, and indeed slew speed was at 1x, and I was unable to change it

Is that intended behavior, or some error? I tried locating some docs but couldn't find any....

You need to set which axis or which buttons control slew up and down in the driver.

If you go to the joystick driver, tab you can move stuff around and it will show which is what.

Ooops, my bad. I really overlooked that menu, although I was searching for it

So seems the slew had been set to one of the analog axis that was outside the dead zone and permanently dragged it to 1x.