This is puzzling me. The problem is likely the resistance in the 4m wire (8m in total to the switch and back). Noise would cause false triggers and doesn’t explain a switch not working at all.
But even with very high resistance (let’s say crazy 100 ohms) the pull down will still be “stronger” than the (guessing >1K) pull-up in the Mini and should win… even over a long wire run.
But what of the Mini isn’t “weak pull-up”, with the switch pulling it low, but instead puts 3v on the one pin and expect to see 3v on the other side through the switch?.. like through an opto-coupler led maybe? In that case just a few ohms in the wire can drop the voltage to below the trigger voltage. That would be very weird design though and I would be surprised if they did that.
One thing to try is to put a potentiometer across the switch pins on the Mini side and “tune” it to a level where the switch reliably triggers the input. This is “floating” the input though and now you might see false triggers caused by noise. It will be interesting to know at what resistance the Mini triggers… turn the pot until it triggers and measure the resistance over the pot (disconnected)
I’m really curious what you find.