An underwater GFCI doesn't matter
That is to say, it doesn't perform any useful function underwater. It does nothing to prevent the water from being electrified, which is its one job. Here's how a GFCI is laid out.
As you can see, if water can get to the "Line" side of the device, then it electrifies the water. And the GFCI cannot do a thing about it.
So this is a lost cause. I really don't care whether your friend thought he saw a GFCI down there; if it exists it is useless.
Besides, having a "test" button in such an inaccessible location is a blatant code violation. It simply makes no sense, unless it's a holdout from the early days of GFCI requirements - maybe it's something the light manufacturer put in there to CYA. Regardless: treat it as if it doesn't exist.
GFCI and overcurrent are different things
A breaker trips on overcurrent, when the total current flow exceeds the breaker limit by a wide enough margin or a long enough time. (breaker trip curves are pretty generous).
A GFCI actively looks for current differential on the two conductors. When it detects a small amount (8ma) of unequal current, that means current is seeking a third path, and it trips.
While they both relate to current, that is the end of the similarities.
That said, if the breaker is a combo GFCI+breaker device, it may seem like an overcurrent trip. You have to pay close attention to its indications to see whether you are dealing with a GFCI or overcurrent trip. If it is a GFCI breaker, it will have a TEST button.
Otherwise if the breaker tripped, it's because either a massive amount of current flowed, or the circuit was mildly overloaded for awhile. This could simply be from too many appliances plugged into the circuit.
GFCI protection is required for pool circuits
As said, the GFCI units underwater don't count. Every circuit within 6 feet of the water (length of a common appliance cord) needs GFCI protection. Fortunately any GFCI device can confer GFCI protection to devices down-circuit of it. At extremes, a GFCI+breaker protects the whole circuit.
So the right way to protect the circuit with the pool lights is find a point along that circuit before it nears the pool, and fit an appropriate GFCI device there. E.G.
- a receptacle not likely to be splashed with water,
- inline in GFCI-only (deadfront) devices,
- part of a GFCI+receptacle+switch combo device
- a GFCI breaker to replace the regular breaker.
Alternately, make the pool lights low-voltage DC
12 volt DC power is incapable of shocking swimmers. Old incandescents draw too much current for that to work with existing wiring, but LED is so efficient that it works fine at 12V on existing wiring. So why have special devices which require constant testing to protect swimmers from shock, when you can moot the entire point by switching to 12 volts DC?
I recommend fitting a 12VDC power supply at least 6' from the pool and running all the pool lighting on that, using LED. This also means you never need to change another bulb. It's even possible to do it using existing fixtures, since they make Edison base LED replacements that are 12 volts DC.