Has anybody experienced repeated failure of the illumination control module/light switch? Replacement units work okay for a month or two, then they burn out without blowing any fuses.

 

There are no fuses going to the ILM. Power comes directly from the bus fuse located in the small black box near the battery.
You might want to do the inline fuse fix. If the ILM is messed up it could cause a fire. Installing inline fuses can help prevent that and may help to isolate your trouble.
Here's my post on how to do the inline fuse fix: ILM Inline fuse fire prevention

 

I would try to find the source of your problem.

With everything turned off place a amp meter between the cars battery ground fitting and the negative battery terminal. Pull the lighting fuses on the side of the dash until the amps drop to .05 or less. The fuse that causes the amp drop is the wiring that has a problem. Fix that and you will stop burning up your illumination module. Here is a link to detail Pizza's Tech Help

The inline fuse is of course also a good suggestion while you are in there making repairs.