We have different boats but Yanmar supplies both the motor, and the wiring loom for the motor, to all manufacturers.
From the Yanmar 3GM30 manual, here is how the power runs for the start circuit:
From the battery positive to the battery switch;
From the battery switch to the starter (fat red wire);
From the starter terminal with the battery lead, through an inline 30 amp fuse, to the key switch (red wire);
From the key switch, via a short white jumper wire, to the push button switch;
And finally from the push button switch, via a white wire, back to the starter solenoid terminal.
Boat wiring is generally stranded vs. solid. Wire will carry enough current and show voltage if only one strand is intact and the other strands are broken. This would allow you to get a voltage reading at the key switch but not enough intact wire to allow sufficient current to “power” the circuit. I suspect that you have a break (all but a strand or two) in the wire that runs from the starter to the key switch. It could also be a partially failed 30 amp inline fuse.
As a simple test, run a length of 12 gage wire direct from the battery positive to the red terminal on the key switch. This will isolate the feed side of the circuit. If your problem goes away, then you know where to look.
OK … Here is the “intermittent no start” problem. The “white” wire that goes from the push button switch to the starter solenoid is, at best, marginally adequate to feed the current needed to energize the starter solenoid when the boat is new. The circuit naturally develops internal resistance with age. This increased internal resistance, combined with undersized wire, reduces the current flow through the white wire. The result … When the starter starts to turn, the current draw causes a voltage drop just big enough to disengage the starter solenoid.
A number of us Beneteau owners have installed a Ford style automotive starter relay to eliminate the problem. The white wire just triggers the relay vs. powering and holding the starter solenoid closed when the starter cranks.