Shurflo fresh water pump
You would do well to go to the Shurflo website, they have troubleshooting tips & tricks.
You most likely have the Shurflo 2.8 GPM -- Model # 2088-423-344, which Catalina and other builders put into most all of their midsized boats. That is what our 1986 boat came with.
A few years ago Shurflo discontinued that
pump and replaced it with Shurflo Model 3901-0216. It's pretty much the same
pump, same mounting feet and screw dimensions, and same water hose connectors, although you may have 90 degree elbows on the existing
pump, the new
pump comes with straight barb connectors, but you can reuse your old ones. It all depends on your layout.
Old pump: 2.8 gpm, 45 psi, New Pump: 3.0 gpm, 55 psi. Essentially the same.
You could also go to a new variable flow pump. Your boat, your choice, but the same footprint will make it easy to swap out.
I know all this stuff intimately, because I was working on it just last week!
My symptoms were a bit different than yours: my pump continued to cycle even though, after thorough checking, there were no leaks in the pipes, full tanks, no faucet leaks, etc. The pump always performed perfectly. We did not have any pump starts after it was off even with the main breaker on for the 15 years we've owned the boat. Rather suddenly two weekends ago it started acting up. It would pump water, but not shut off without the breaker being turned off.
I have concluded that the pump is bad. After 26 years, I figure both the PO & I got good service out of it!!!
It's a diaphragm pump and the three little water pump diaphragms do and can wear out. We use our boat weekly,
anchor out and use that water pump liberally.
If the suggestions here & the Shurflo website don't help, you've done everything you can do.
If you can't fix it, then the other option is to buy a new pump!
I bought our replacement pump on sale in 2010 (I like to have backups just in case we're in the boonies when stuff breaks). My records show I paid $98.76 for it. You could find a good online price, better pricing at RV stores than marine.
Good luck.