The terms "fuse" and "circuit breaker" are not interchangeable although they perform the same function in most installations. I have never seen a residential electrical panel with both fuses and circuit breakers included as original equipment.
So do you have both or just one of those types of overcurrent protection? And if just one, which one?

Sorry. No fuses in the box.

No mention is made concerning if the LEDs have been disconnected. The first step in diagnosing tripping problems is to remove all loads and then determine how the device is functioning -or not.

LEDs are currently disconnected. The pump is working fine. My question is, is it unusual for both the GFI and the breaker to trip. And, is this an indication that the breaker should be replaced or just the GFI? I guess I'll start with the GFI and go from there.

This post was edited by jrb451 on Sun, Aug 3, 14 at 10:50

The GFI and breaker serve two different functions. The simple description of the GFI is that is compares the current leaving with the current coming back. If they don't match, some current must be going somewhere else (like through you), and the GFI trips. It trips for even a small difference. On the other hand, the breaker protects the wire from too much current flowing through it even if the current going out matches the current coming back. A GFI wouldn't trip for a direct short from the 'black' to the 'white' wire, but the breaker would trip.