Pool cover motors and ground fault

I have had an auto pool cover for about 5 years and this year it has developed a nasty habit of tripping the ground fault when it gets really wet. Hasn't been a problem since June, but it reared its ugly head again. The way it is wired, since the cover was put in about 18 years after the pool, it shares a circuit with the pump. Needless to say I can get by w/o the cover while it dries out, but the pump is necessary. I am trying to not put the cover on a separate circuit. If I unplug the motor for the auto cover, the GFI is no longer a problem and the pump runs fine. I am wondering if liberal doses of silicon spray around the areas where the wires plug into the motor and the box they come out of would solve this problem? The main culprit, at least to my limited troubleshooting, is likely to be the gaskets around the box. Any other suggestions?
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Have you opened the box to see if any water is getting in? You could also possibly put something over the whole thing, like a garbage can, when it rains to verify that it's in the motor/box area and not something totally different.
I'd look for any possible water infiltration points and use silicone cauk on them, but only after it's been dry for days.
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Is the GFI a breaker or a receptacle? If it's a receptacle you might try replacing it. They do go bad i.e. get more sensitive.
I suppose GFI breakers go bad also, but I think receptacles go bad more often, percentage wise.
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