How about vibration sensor? Unless you push the button gently, the sensor should be able to pick small vibration.
I believe that would be interesting if you are near a road or railroad where trucks or trains may shake things around. Not the case, as the intended generator is a warehouse.
I saw some people creating random number generation with Geiger counters, using radioactive decay as an entropy source.
One guy Alex Waltz even went to extreme with his project and he combined Raspberry Pi, Geiger counter, Audio interface and Americium 241 from a Smoke Detector.... I think that plain old dices would be just fine Smiley
https://twitter.com/raw_avocado/status/1433408813596545027That's quite interesting too.
Updating: after checking some waves around, I'm now thinking on use AM or SW bands rather than FM.