I have an issue with a gfi and some post lights.

Setup. I have a dedicated circuit that come from the panel to an intermatic switch in the basement. The switch then powers an outlet in the garage. Here, a 12v low power landscape light transformer is plugged in. The line voltage wire continues across my yard to a GFI in an outside protected outlet. It then powers 2 post lights with 3 bulbs each.

problem:Sometimes, mostly after it rains, the gfi trips. If I push on the "reset", it just trips again, even days later. If I remove the 6 bulbs, I can reset it, put the bulbs back in, and then it works for a few weeks. It trips again days later, again, usually when it rains, but not always.

questions:
1. Shoud the GFI be INSIDE the garage protecting the whole line outside the house? shoud it protect the transformer?
2. Is the Intermatic somehow tripping the GFI? I have seen posts where this was suspect. Should I move the timer after the GFI?
3. Maybe it's a "pinhole" power leak that only crosses the gfi threshold when its damp out?

any suggestions welcome.