I have the same MH as you. I don't think there is a check valve on the gravity fill port. The water will slosh around when driving and come out the port, at least it does on mine.
When you fill the tank you maybe over filling the flexible tank and as it returns to it's normal shape size the water will come out the overflow or the gravity fill. You could open the outside "shower" and relieve some of the pressure without putting it in your tanks.
My pump also will cycle occasionally, or if turned off for a bit will pump for a second or two when turned on again. I don't have any water dripping inside that I know of so I don't really worry about it. I don't know if there is a check valve from the tank to the pump which could possible have a bit of an internal leak back into the tank.
The tank level indicators are known to not be calibrated, at empty I can still get a shower and have water in the tank.
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