Assuming this is an older house, it likely had old cloth Romex which would've needed a conduit to conduct ground if plumbing was not near. The red/gray/black combo looks like it was updated at some point.

Sounds like you've got a Chicago 3-way setup. Especially since it's an older house, literally in Chicago. It can be used for non-3-way stuff, but this was most common for a jumped/shared neutral.

https://youtu.be/qjOth4dnMxo

The issue with your switch is that it relies on a dedicated ground and neutral circuit (which you don't have). Had this problem in my 1950s house until that circuit was rewired to modern standards.

Simple solution: skip the illuminated switch.