Should I only run my bilge pump when the engine is off...or can it run
safely when the boat is under power and running?


Your bilge pump should be able to run any time, underway, anchored,
docked, etc etc.

Marshall Banana wrote:
It's OK either way. If you store your boat in the water, and you have an
automatic float switch, it's not a bad idea to install a cycle
counter. It counts each time your pump runs, so if you develop a small
leak at a fitting, you will see a large increase in the number of cycles
on the counter.

A cycle counter is a good idea... so is an hour meter. A little red
light on the dashboard, or the electrical panel, or somewhere else where
you will see it & notice, is also a very good idea.

Some people hook up alarms to their bilge pumps, but I think this is
going a bit too far IMHO.

Fair Skies
Doug King