My boat has a skeg for the rudder and I think it is hollow. You would think that would be easy to check, but it is under the fuel tank and fairly impossible to get at. I suspect it has water in it, cause every now and then after racing (only when the boat is well healed) I get some water end up in a locker near the stern, even if the bilge is empty.
What would be the best option? Put in a separate bilge pump, somehow feed a hose down and just run it with the normal bilge pump? Or drain it (somehow) and fill with expanding stuff (which would probably pop back out again)?
I don't think the tank can be moved, can't see any retaining bolts.

Is that a packing gland at upper end of the rudder tube? My Adams 31 used to leak there a bit. As MB said, a dry gland at anchor then water forced up when you heal, likely the gland seals ok once its saturated, but it could be worthwhile replacing packing material - if it exists.
Thanks for the advice, hadn't thought about the packing gland as the culprit. Will check it this weekend.
I might also buy a cheap pool Ph kit and check if the water is fresh or salt.
I have an autopilot to connect to that shaft in the next few weeks, so would be good to get it fixed before then.
I spent a fair bit of the weekend tracing water droplets. The good news is the rudder gland does not leak. All the water in the back tank is fresh water. After putting many buckets of water over the deck, we found 1 of the 3 sources of the water. So that has been temporarily fixed, will require tools I didn't have to fix it properly.
Still have 2 other leaks, 1 of which would appear to be rear port hull window at the nav station. Or perhaps the staunchion on the rail, but the window appears to be the culprit. Yes that one is salty, but it is running down the wall directly to the bilge via the base of the nav table.
The 3rd one has us beat at the moment. The water (fresh) runs across a bulkhead behind the nav table and drips into the left locker shown in the photo. Only happens in reasonably heavy rain. The other 2 lockers stay dry. The bulkhead is higher than the toe rail, so unless water can run uphill it is not coming from there. Thowing buckets of water across the deck and around the dodger area does not reveal anything. I probably will have to use a pressure hose at the marina and see what I can find.
Any other thoughts?

I had a tricky leak that pooled in a locker 2m aft of the culprit. It was a leaking screw from the alloy toe rail.
You had a win that's a good thing
, only 2 more to go. I feel your pain I got sick of getting a wet bed and ended up ripping out all the lining in my aft cabin.i think I found the leak lol.