Meanwhile I got an answer from Olivier Beaute.
I've seen this case twice on an AMEL 54. In both cases, the vessel suffered a serious grounding and was at first poorly repaired.
I don't believe the water is coming from the rudder shaft tube glassing. This tube is made of thick and plain GRP, glassed to the hull and threaded inside in order the nylon nut (stuffing box) can be tightened.
There are several possibilities for the water to get into the skeg and make its way to the bottom of the rudder shaft tube.
The main ones and easiest to repair are the bolts for the pintle bearing, intermediate bearing of the rudder, and the SSB ground plate bolts. If these bolts are not caulked correctly, some water can make its way around them and migrate to the top of the skeg. This water may also follow the copper strap for the ground plate or the copper strap for the rudder stainless steel supports (that you see on the rudder shaft tube).
If there are other cracks in the skeg, the water may penetrate and go into the foam that is inside the top part of the skeg, and then through the GRP covering the top of the skeg.
The skeg is originally part of the hull. Once it is built, it is filled up with polyurethane foam and the top is glassed (with woven cloth) to the hull.
The worst you may need to do is open the skeg from the side, remove the foam, glass all its inside edges with new glass cloth and epoxy, and put new foam and close the skeg.