Thanks for all the info. I am familiar with the toilet and the wet/dry
mode. That definitely isn't the issue as I move the lever to dry after
each use. Even in the dry mode, water is entering the head.

As simple as it sounds, I believe the issue is that I've been leaving
the seacock during the week when I'm not using the boat. I guess I
need to close the seacock between uses as well. This is inconvenient,
but possible as I have pretty easy access to the seacock.

I am still not sure about the second pump that I have. I will take
pictures and send, but here's a bit better explanation of if:

The pump is a hand pump similar to a manual bilge pump. It forms an
upside down "T".

1. Hose enters boat through seacock and does a loop to about 5' in the
air. This is a 2nd seacock - not the one used for water to enter the
head. It is also larger. Probably 1 1/2" hose vs. the smaller used
for the head intake.
2. It goes back to form the stick part of the T.
3. On the "across" part of the T (bottom of pump), there is flow going
from holding tank to the pump out access on the deck.

I am assuming this is used to help push the material out and to flush
the system.