I would take it apart and be careful , good chance it just needs cleaning and can reuse the gaskets etc
look for what the problem is and what is needed before buying parts
for the bowl to over fill, something has to keep the float from seating the needle into the seat to stop the flow of fuel when the bowl is full.
or debris is in the seat keeping the needle from sealing off
sounds like that is a vent and the carb is over filling.
time to take the carb apart and see what is keeping the float from closing off the needle and seat when the carb is full
run some weed wacker line up it to see if that clears it ,
if not blow some compressed air up it while it is idling on the muffs or in the water.
small insects like to make nests up inside those small holes
Loose drain and vent will let some in if it has sat in water and run since it was serviced.
I would run it for a few hours in the water as normal and check again to make sure it is not getting water in it.
make sure to drain it into a clean container so you can put it back in if no problems...
I am thinking he is looking for the part that connects to the 10 pin (or six pin according to pic) harness that has the bullet connections on the wires that plug into the ones on the 704
did you make sure the shift shaft lined up with the top part as you put the lower unit back on?
bottom part will not turn if they are not hooked up to each other.
it you moved the shift shaft while the lower unit was off , you will need to take it back off and make sure both in neutral or the...
check for spark and timing with a timing light and also open the drains on the carb bowls to see if they have fuel.
need good compression,good spark at the correct time, and proper fuel to air ratio in the cylinders to start and run
never heard of a motor that would not pump water out of the Tell tail when running on muffs
is this an after market kit you bought?
Never heard of a Yamaha kit including housing.