Cascading GFCIs makes for difficult troubleshooting.and connected to anouther gfi in the bathroom on the same level.
To check if moist cable insulation is causing the current leakage,
when the tripping condition shows up [or try to induce it with a sprinkling can]
disconnect the ground wire [treat the lifted ground wire as if it were energized] at the panel
and put an AC milliammeter in series with a 1/16A [or less] fuse between the lifted ground wire and the panel ground.
More than 4mA fails and more than ~100 uA is suspect.
Disconnect all appliances on this line first.
The fuse protects the milliammeter's internal fuse.
If it's not the cable, and it is not somehow the disconnected appliances, then it is almost certainly the GFCIs themselves that are tripping from moisture.