The illuminated switch uses a small neon bulb that leaks a few milliamps to light the neon.

They do not operate well with an CFL.

The illuminated switch sends a small amount of power to the "bulbs" in the fixture even when the switch is off. The fluorescents do not "like" that. Remove all the "bulbs" from the fixture and your switch will not be lighted.

Thanks Bus driver, I'm going to pick up a spare
illuminated dimmer switch and do some
experimenting on the work bench.

You should also know that CFLs do not dim as 'nicely' as incandescent lights.

In almost all cases the dimming rage is limited before the bulb goes out.

Yes Brick, I've heard of that, but it's not a problem
because I'm the only one that uses the dimmer. Mother
always has those lights on full bore, even if there is
no one in the room. She doesn't care because she doesn't
pay the utility bills. When I'm gone, she'll find out.