There might be something else going on. I'm going to assume this is a foot-operated toilet like is says on the Jayco Eagle website.
If it was just the valve continuing to admit water when the waste flap is closed, then the toilet would quickly overflow. Unlike home commodes that have no waste valve, unless the flap operated by the spring-loaded foot pedal gets out of the way, there's no way the excess water coming in is going to get out other than over the rim. So I'm presuming the waste valve isn't sealing tightly either.
If you have to replace the water valve (like I did last year when a bad winterizing job caused it to crack) they caution you not to remove anything at the flush pedal hub - presumably because you could mess up the return spring tension.
My money's on something to do with the return spring in the hub. The water valve is activated by a cam integral to the foot valve hub so if it doesn't come back up, its going to keep both valves open. Does it stop when you lift up the end of the foot valve with your toe? If so, it should stay up on its own because the water valve actuator should provide enough pressure on the low end of the cam to keep gravity from pulling it back down.
2015 Rockwood Signature UltraLite 8282WS Platinum, GY Marathon LRD, TST 507RV TPMS
2005 GMC 2500HD CCSB D/A, Curt E16, Prodigy P2, Garmin RV760LMT w/BC-20 b/u cam