That pump is a Berkeley JF. Similar to the JE, the JF had trimable nozzle set up. Both are what is known as an "insert" pump. Not the most desirable for performance but just fine for a nice lake boat. Make sure all the necessary bits and pieces for the controls are there as they are hard, if not impossible, to come by.
BTW, if you look at the top of the pump, inside the boat just to the rear of the thrust bearing housing, there should be a plate identifying the unit.