The toilet in photo
on the left appears to be a Jabsco
on the right is too far out of focus for me to tell what it is. You can see all of Jabsco's toilet here: Jabsco Marine / RV Toilets and Waste Systems
...they've redesigned their website to make finding anything on it as difficult as possible (I've just discovered that NONE of my bookmarks still work), but this page does include every toilet they make. You mentioned a pump
, which would make it a sea water toilet, either 37010 or a 37245. The owners manual for each one is under "Documentation and Tools...they call it a "technical data sheet."
As you'll discover as you check 'em all out, Jabsco
doesn't make a toilet designed to use both fresh and sea water. Toilets that are have TWO inlet flush water inlet fittings, one dedicated to the fresh water supply, the other dedicated to the sea water pump
...that's to prevent sea water from contaminating the fresh water supply. Yours has to be a PO's DIY plumbing
job. So you might want to reconsider whether to keep that setup.
I can only guess how your toilets are plumbed, so the best I can do is tell you how they be plumbed. Toilets designed to use onboard fresh water don't have an intake pump, they're teed into the cold water line to the head
sink and use pressurized water...which means the boat's fresh water pump
has to be on to supply the flush water. There's a solenoid valve in the inlet line that's wired to the flush button...it works like a faucet does--opens to let water run into the bowl when the button is pushed, closes to shut off the flow of water when you release the flush button. When you removed the solenoid valve (they have a high failure rate/short lifespan btw), you removed the "faucet" so there's nothing preventing water from flowing into your toilet bowl. If it was in the vented loop, it can't work
without it either. The owners manuals
for the fresh water toilets should give you some insight into how they're supposed to work
That should be enough to get you started sorting it all out...