I suspect that I also have some wet core around my stanchion bases. I'll be checking into it later this summer. From my experience with wet core around the mast step, and in a few other locations where deck hardware was attached, you will likely have to go through the following procedure:

1. Remove the stanchion base.
2. 2) Determine how far the wetness extends by drilling exploratory holes through the outer skin and core, but not through the inner skin. I used a 3/8" bit to pull up enough core to inspect. Carefully examine the condition of the core that you drill out - if it's black and mushy, it's rotten. If it's wet, butlight brown, then you are near the edge of the wetness. If it's dry and dusty,great, you're past the wet spot.
3. 3) cut away the outer skin of the fibreglass over the area of core that has been damaged, and remove the wet core. I used a 2 1/2 hole saw, because that's whatI had at hand, for my work around the mast step, and removed 3 plugs of outerskin and core. I used some supplementary small holes, some picks and a vaccuum cleaner to get all of the wet core out. If you area is larger, consider usinga sabre saw or sawz-all with the blade adjusted to cut only the outer skin andnot the inner skin. You could then peel off the outer skin, to re-use afterthe core has been repaired.
4. 4) Replace the core with the material of your choice. Because I was working with a few relatively small areas, I used epoxy resin with 1/4" chopped glass fibers to make a mash that set up quite hard. I used colloidal silica fillers with epoxy resin for some even smaller areas. If you've got a big area, you could use marine plywood to form a new core.
5. 5) Put the old outer skin back on, or make a new one by laying in layers of fiberglass and resin. I just put back the plugs that the hole saw had cut,while the epoxy/fiber mash was still wet.
6. 6) Smooth and re-finish the exposed expoxy / fiberglass to your own taste. I mostly covered up my work with deck hardware. There are increasingly effective cosmetic approaches to take, starting with just using off-the-shelf white gelcoat up to professionally matched gelcoat or even a complete paint job.
7. This is all explained in wonderful clarity, with tons of excellent illustrations in a book that you should geat before you start:Here's the book, as copied from http://www.nauticalmind.com/maintain.html,Sailboat Hull and Deck Repair Casey, Don Fibreglass is easy to repair and this volume tells you how to do it. Among the repairs covered are: rebedding deck hardware, replacing portlights, fixing leaky hull-deck joints, and repairing cracks, holes, blisters, gouges, and the other ailments to which fibreglass is prone. 144pp. photos & illus. hc 1995 $28.95 CAN

I offer the following info for those wishing to fill screw holes in a balsa deck and to stop leaks. I have recently been doing this on my 1976 33. The process goes something like this:
1. Put an allen wrench in a drill. 1/16 inch wrench should work, depending on bolt hole size in the deck. Angle the short side of the wrench into the hole and run the drill untill you have ripped out all the core. Have a good vacumn handy to suck out the debris.
2. Find some kind of clay like puddy at the hardware store to make a temporary plug for the underside of the hole.
3. West Marine sells their own brand of epoxy which is a good deal less than West. They have a specific product called a penetrating epoxy. I would recommend you put some of this into the hole to penetrate and seal the balsa. This is very thin and will find leaks very well. Don't put in so much that you completly fill the hole. Even if you do it will probably soak into the balsa and leave a void to be filled later with a regular epoxy. Wait 24 hours.
4. Finish filling the hole with regular epoxy.

This process creates a good seal and keeps the balsa from colapsing when you install a fitting.