Instrument panel dimmer knob removal
The knob actually has a lid cap on the front (the area where they screened the graphic icon). They did too good a job there, so you can't really see the gap -- unlike on the dash, panels, etc.
With a lot of luck, and a really tiny flat head screw driver (jewellery type) or scalpel blade, you might be able to open the lid without damaging the knob.
There's a nut holding it inside. You could tighten it up once you have the cap opened. To get the lid out is the tricky part.
Once this has been removed, you can see the potentiometer shaft behind. If the potentiometer is suspect, Farnell offer an almost identical replacement part: Farnell UK link. In case this link stops working, it's manufactured by Vishay-Sfernice and their part number is PE30L0FL103KAB It can be seen side by side with the original here (original part on the left):
The threaded section is slightly larger diameter than the original, while the end of the spindle is marginally narrower. It comes with a panel mounting nut and washer so this difference doesn't matter. The narrower spindle can be overcome by wrapping the end of the spindle with a single turn of electrical tape. This allows the knob to grip it properly.
In my car this was taped with electrical tape to a parallel section of wire - the tape can be carefully pulled off or cut, being careful not to nick any other wires.
Carefully remove the heatshrink from the connectors, then desolder the wires. One or more may already be loose - explaining any problems!
Follow the wiring diagram here when re-soldering the new potentiometer - the connectors are all the in same place as the old one so can easily be transposed across.
Refitting is reverse of removal!