I'd think it's quite unlikely that your fan switch has failed, even with the rotation you describe*. You can test it easily enough though.
Here's a VW one I dissected recently, and the electrical (left side of pic) stuff has no wiring that would twist and break if it is rotated relative to the brass casing. It would just indicate that the brass 'crimp' hasn't been done quite tight enough down onto the plastic.

If the Omega one is internally the same-ish, and has the same dual contact arrangement you can test it with a multimeter. You may well find that the external contacts are labelled something like + (or 0 ?), 1, and 2. At around 95C the + one should become connected to 1, and at about 102C contact 2 should also connect to +.
You may need to take it off the rad and warm the brass bit with a hot air gun to get to 102, as boiling water won't quite do it for you, but the 1st switch should click at less than 100C.

*Edit: unless it's really loose, as that would affect how far the moving plastic peg has to go to push the contact mechanisms :-/