I also have a '91 V-20 that has the same fish box that you discribe.
It has an inline pump connected into the drain hose from the fish box
that discharges overboard. The pump looks like a small bilge pump
except that it has hose connections on both input and output. It is
turned on by a dash mounted switch marked "pump" that looks original.
The pump is accessed through a pop out deck plate type hatch that is
inside the fish box in the rear wall.

I just bought my boat last November and only had a chance to use the
fishbox for fish one time before pulling the boat. There seemed to be
a problem with the pump; it turns on and runs, but only pumps a trickle
of water out the discharge. The pathway doesn't seem to be blocked
because if you shoot a garden hose into the fishbox drain the water comes
out the discharge through hull fitting full force. This is a problem I intend
to fix this spring; I 'm guessing that the pump needs to be repaired or replaced.
If your still interested, when the time comes, I'll post the make and model
of the pump.