Sconce light flickers when fan rheostat is turned.

[Heathdemps]

A month ago I installed a dimmer for a sconce. There had been a switch there originally. Dimmable LED bulb, rotary dimmer, everything worked perfectly with the caveat that the LED goes off a bit before the dimmer clicks off. No problem. Except a guest didn't turn the dimmer until it clicked off, just until the bulb was off. A couple of days later the HO turned a ceiling fan on with a rotary rheostat and the sconce flicked on for a second then went out. The rheostat is on a different wall from the dimmer, but closer to the sconce. Rheostat is the middle device in a bank of 3, doesn't affect the fixtures connected to those dimmers. I played with it a bit, found that even when the LED is on partway it brightens when the rheostat is turned, but not every time. Tried an incandescent, same thing. Almost everytime this happens the fan makes a brief buzzing sound. Apparently this sound has been going on for some time, but the light situation never came up because it wasn't dimmed before. The original rheostat had 3 speeds and off. Sound and light flicker happens when switching between speeds, or even putting pressure on the dial but not turning it enough to click to the next speed. HO wants to stick with rotary so I bought a new one. This one didn't have positive stops to adjust the speed, and the fan hummed a bit at any speed except the highest. Tried another rotary rheostat with 3 speeds like the original and it did the same thing as the first. Went back to the 1st replacement and found that the light flicker and buzz sometimes happen when turning it on. That's the only "click" that happens with this rheostat, unlike the original and 2nd replacement which click everytime the speed is changed. That's where we left it for now because I'm stumped. Sconce and fan are on the same circuit but, aside from that, there's no connection. One of the dimmers in the same box as the rheostat is also on the same circuit and is not affected. The other dimmer is on a different circuit but controls sconces identical to the affected one, but they aren't affected. There is 3wire from the box to the fan, but no fan light so red wire is capped.
Sorry this is so long, but I'm trying to give every piece of info that might help figure this out.