On your boat, a toilet teed into the head sink drain line would be a PO (previous owner) modification--one that I highly recommend btw...but yes the head sink drain seacock would have to be open. Which, if your sink drains ok, it must be. So I doubt if that mod was done on your boat.
Depending on the make/model/age of your toilet, if making sure the toilet intake thru-hull is open and the toilet is in the wet mode doesn't solve your problem, it MIGHT be time for to replace the toilet pump. If that turns out to be case, there's something else worth considering: replacing the whole system with an MSD portapotty.
On any boat much smaller than about 28', a self-contained system—an "MSD" portapotty-- makes a lot of sense. The "MSD" designation in the model name/number means it has fittings for a pumpout line and vent line, and is designed to be permanently installed (actually just sturdier brackets than portables, so you could still take it off the boat if you absolutely have to), which means that although it's still called a PORTApotty, you don't have to carry anything off the boat to empty it.
A 5-6 gallon model holds 50-60 flushes...you'd need at least a 30 gal tank to hold that many from a manual marine toilet. No plumbing needed except a vent line and pumpout hose--so no new holes in the boat...and -0- maintenance needed except for rinsing out the tank--which you can do with a bucket while it's being pumped out. Total cost including the pumpout hose and vent line is about $200--a fraction of what you'd spend for toilet, tank and all the related plumbing needed. And the best part is, you have all the advantages of a toilet and holding tank without giving up a single square foot of storage space.
Check out the Thetford 550P MSD and the Dometic/SeaLand 975MSD Sanipottie
Just a suggestion...
--Peggie