Just got my K100Lt last week, still on my first tank of gas and found that with 100 miles on the trip counter the gas warning light comes on every so often.  The gas gauge does not work but I can see fuel in the tank.  I brimmed it to the top when i first drove her home.

This normal?

No, that doesn't sound normal...i bit early...mine comes on after ~300 km.

But when going in areas with much hills it can go on and off multiple times
before it stays lit.
But a long uphill is needed to make the warning lamp turn on, as it got a
built in delay in the circuit.

This was a problem on much earlier models than you got, with a different
level reading system.

Since your gauge also doesn't function,....it could be that a PO have done
some adjustements.
Here you got good description about the Level sender, by Robmack:
https://www.k100-forum.com/t3349-testing-in-tank-fuel-sender-unit#76423