Cheshire wrote:
As best as I can tell, nothing's unattached.
This is where it gets hard to remotely diagnose a problem.
Maybe someone with experience knows of a simple check to see if the gauge itself is working. Often there is a simple test where one grounds a wire at the sender with key on and the gauge will go to the highest reading. I would hesitate to make a guess on someones scooter.
Two other thoughts are:
Is the engine really warm? My question is if the thermostat is working allowing engine to get up to normal temperature. One wa to know if if you could take a reading at the thermostat housing with somethnig like an infrared thermometer:
https://www.harborfreight.com/infrared-thermometer-93984.html
The other idea is if the engine is in fact getting up to normal temp and the gauge and wiring to it are good then the sender may be at fault.
Please note these are just thoughts and not saying what the actual problem might be.