I've got water seeping out of the outside of our fiberglass tub/shower enclosure (the rough-finished side enclosed in the wall) and damaging the ceiling below. The water is coming from a overhanging contour point above the overflow but below the control handle. Can water get inside the honeycomb-like liner?

I see no cracks in the tub/shower interior. But recently I found a leak in the handle escutcheon, which now seems to be fixed. I'm wondering if that leak could have allowed water to get inside the fiberglass via the edge of the hole through which the shower handle goes (and the escutcheon seals). And now the water that's built up inside is working its way through to the surface. Mineral stains on the liner make me think this has been going on for a long time.

So assuming there are no remaining plumbing or fitting leaks (cross fingers), should I try drilling into the liner and draining the water?

Thanks in advance for whatever advice you can provide.