I have no idea if your boat is a fishing boat, a runabout, or a combination so from your description it is hard to tell whether what you think is a livewell really is. It may be nothing more than a cooler. Put ice and your drinks in there and the liquid goes down the drain. If it was a livewell, there would be a switch on the console that says "Livewell". That switch activates the pump that pumps water into the livewell. If this is really a livewell, it would have a tube or spray head near the top of the tank either on the front, back or either side. A standpipe would be required in the drain to serve as an overflow. If a simple plug was needed to keep water in the livewell, then there must be an overflow to dump excess water overboard. I really think you have a cooler and not a livewell. Check for the switch.
