One tip. If your boat is like the '57 King Commander my dad had (and which my son still has) there are four small (quarter inch in diameter or smaller) bolts across the back just below the wooden part of the transom. For years that boat leaked a little bit when it was sitting still in the water. It didn't leak when the boat was underway. We checked for loose rivets. There were no loose rivets. We checked the drain plug. Nothing wrong there. It was a mystery that we couldn't solve. There wasn't enough leakage to be dangerous, but it was an annoyance.
One day, quite by accident, I noticed that the nut on one of those small bolts was loose. A screw driver and a crescent wrench cured the problem. Apparently the weight of the motor weight was just enough to submerge those loose bolts when setting dead in the water and let a little water in.
Since then I've heard similar stories from a couple of other 50s model Lone Star owners.