The dripping fuel could be leaking needle/seat. It could also be a crack in the brass overflow tube inside the bowl. It could also be the drain plug/gasket.
Maybe turn off the petcock and see if it still happens. If it doesn't leak, blame the needle/seat. If it does, blame something else.
The consensus is to use Honda parts. They are mostly available, but expensive. I used partzilla.com and delivery was quick.