Bill, yes it will bolt on but watch the outlet nipple.
The square pump is the one OMC used on the small twins for years. Same two hole pattern on the bypass cover, that is why the parts book lists it for your motor. It comes with a gasket and the two screws.
What gets people is the outlet. On the square pump that barb points the other way than it does on your five sided 304039. If the line has to make a hard bend there it will kink, and then you chase a fuel starvation problem that was never the pump. Leave yourself some slack, or run a longer loop of hose.
Check the gasket too. The pulse hole has to line up with the hole in the bypass cover, and the passage in the cover has to be open. I have found those plugged with carbon and old sealer before.
One more thing. 304039 is not in the supersession chain for 388685, so nobody is going to hand you a straight replacement number for it. The square pump is the practical answer, it is just not a hang it and forget it job.
I could be wrong about your exact cover, some of that 64 stuff changed mid year. Put up a picture of the cover with the pump off if you want another set of eyes on it...
thanks