[Descant]

I'd get a hose, add some water to the bilge and see if the pump turns on/off automatically and otherwise operates as advertised. Does the bilge pump switch have a manual/auto position? Again, try both positions with added water.

It seems unusual that the very short cycle time you describe would be a properly operating bilge pump. I used to have a dripping stuffing box. The pump waited for enough drips, then ran for 30 seconds or so, then shut off. No problem, just tighten the stuffing box as needed.

Were there any accessories added by a previous owner that may have bypassed the fuse panel and tapped into power someplace else? I'm thinking a head or water pressure system or windshield wiper. Anything with a small servo/motor. My car had a CD player that made that sort of noise every so often. Caused by inserting two CD's into the changer where only one was intended.

Oops. Missed that OP is the first owner.