First off..........rv toilets shouldn't have any bead of caulking around base.
Toilet uses a foam floor flange gasket to seal. Caulking unnecessary and would just crack due to movement of RV. Replace toilet floor flange foam gasket and clean old caulking off.
Leak also could be from toilet water valve and/or vacuum breaker.
Lay couple sheets of TP on floor under water valve...check for wetness.
May need new assembly
Water pump cycling w/o any demand means there is a leak.
Disconnect pump suction line.......plug it. No more pump cycling then pump internal check valve elaking allowing backflow thru pump.
You can istall an in-line check valve ($10) in pump suction to stop that.
Is it time for your medication or mine?
2007 DODGE 3500 QC SRW 5.9L CTD In-Bed 'quiet gen'
2007 HitchHiker II 32.5 UKTG 2000W Xantex Inverter
US NAVY------USS Decatur DDG31