Do NOT use caulking. Eventually it will come free of the fiberglass and allow leakage into the core.
Use raw, unthickened epoxy to wet the core and the fiberglass. Then wet some cloth and then lather that cloth with thickened epoxy and roll it as tight as you can and stuff into the hole. There will be lots of squeeze out so be prepared.
Then once the cloth is in the hole tape over it and using a hypodermic needle filled with lightly thickened epoxy poke a hole and squeeze as much of that thickened epoxy into the hole as it will take continuing to gently press the plunger as you withdraw the needle. Let it set up for a day or two and remove the tape. You can sand it smooth after or as suggested use a dremel carefully.
If the hole is quite small then you may not be able to use cloth. Then use the minifiber filler to thicken the epoxy and use the hypo to inject and fill the hole.,,For small hole wetting a few pipe cleaners work very well.
But wet the hole with unthickened epoxy first regardless.
The use gelcoat to colour and disguise the hole. This will be a permanent, reliable repair.
I know , and I've said it myself, that wisdom says you cannot apply gelcoat over epoxy but according to a recent article from Gougeon Bros., West System Epoxy, that is not so.
Carefull prep is needed but apparently it can be successfully done.
Free Gougeon Bros mag. Number 42, Spring 2016.
Applying Polyester Gelcoat over Epoxy | Epoxyworks