Thanks, Poconos. A friend came over today who is much more adept at this things than myself. He read your note, and also contacted a friend of his who is an electrician. The electrician wrote this note:
"Based on when it shorts it means the wire it crimped at some place (could have happened when the wire was removed and put back in during the resurfacing of the pool) or is corroding in a spot, causing a higher amount of resistance in the line, which trips the breaker. So, the only way to fix it is to locate the crimped wire, and cut it out."
My friend checked the resistance, checked the wires that are not inside the tube going from the breaker box to the pool, dried out the fixture once again more thoroughly than I had done myself, and disconnected a second wire attached to that circuit (which was for an exterior light above the pool that has not worked since before we bought this house 8 years ago). Put everything back together . . . and the light stayed on for 20 minutes, longer than ever before this season, but still eventually tripped the GFCI.
I guess replacing the GFCI would be the next step, right?