I wouldn't expect to see any leaks from the keel itself. The only place there could be leaks are through hull penetrations (i.e seacocks, stern gland, log transducer etc.).
That said, there are of lot of places from where water split inside from areas such as under heads sinks or behind lockers etc. where water could be pooling in the hull.
A leak stopping when sitting on the bottom appears strange - that could imply one of the penetrations may be loose and, when compressed by sitting on the bottom, closes up. It could also be from a hull penetration near the waterline which comes out of the water when sitting on the bottom.
Definitely requires deeper investigation in my opinion.