Veeerrry Interesting !
Per the owner bio, this boat is an E-32-3 model. That's an 80's boat and the one I have been aboard has a foot pump for fresh and also has pressure water. There may be an accumulator, but some sistership owners will have to chime in on that. The factory did
not put in an accumulator in our '88 boat, and I added one later.
There is a vent at one end at the top of each water tank (or maybe on the top surface... and that vent is plumbed to a spout on the counter for discharge into a sink or basin.
No way should any of those vent ever spout any water unless you are filling via the deck fill pipe and put in the maximum amount to the overflow point, IMHO. Now I remember reading here somewhere that some of these models have several water tanks and may have more than one vent hose T-ed together and thence run to one overflow tap.
The easy answer would be to say that running the pressure pump cannot cause what is being described... but since the symptom is real... there's gotta be a reason. Time for some exploration under the counters and following that vent hose all the way back to the top of the tank.
As to the constant pump cycling, ours did that too until I added the accumulator.
Keep us posted, and you other sistership owners can join in any time!
LB
ps: do a site search on the word "accumulator." Some good threads here already.