My K1100lt stays just at the edge of the red for temp.
Where should my gauge be staying while riding? At the edge of red even during cool mornings.

Not really, i would expect it to be mid green. ideally. you dont say if fan kicks in or temp light comes on so i would check coolant mix, test thermostat, just to be sure.
PS worth testing temp gauge as well

Fan does come on, no temp light. I just don't remember
seeing it run this hot. Is there an ohm test for the gauge?

On my bikes, the BMW temperature gauge needle stays around the 11 o'clock position when moving.  When stuck in traffic it will go to the 1 o'clock position.  About half way from there to the red the fan will come on and the temperature will come down to the needle at the 12 o'clock position.

If your gauge is reading high, are you sure the engine isn't overheating.  The cooling system on K bikes can be a little marginal in hot weather.  If the passages in the radiator are coated with mineral deposits from a previous owner who filled the system with well water or the fins are full of bugs, the radiator's cooling efficiency will be reduced.  It's also possible that the thermostat isn't fully closing off the radiator bypass when the engine comes up to operating temperature.

Two years ago I replaced the thermostat and coolant. Just as a preventative.

Might be a good idea to do a cooling system flush ,and ditto on #4 with cleaning bugs out.
One other thing , Check the hose from RAD to HEADER TANK for blockage or kinks