First check is where is the water actually coming from? If it is actually coming from the transom I would remove all the fasteners and the stanchion. Allow the water to drain and the transom to completely dry out. When the area around the holes seems to be dry mix some west system epoxy, use a syringe to inject epoxy in the holes. When the epoxy is cured re-drill holes to proper size for mounting screws. Use a underwater sealant Boat life or 4200 to seal screws and stanchion.
The other possibility there is a porous weld. The stanchion is full of water and leaking around the screw heads. I have seen that before. I have seen the stainless steel tubing crack from freeze because the tubing was full of water. I would remove the stanchion for both inspections.