thanks for the replies. Yes I have jumped the starter with a wrench and the mower strarts and runs fine. I've tested the solenoid it works fine when battery voltage applied directly to the coil. I also put a new solenoid in and still get click no crank. both solenoids test fine on a bench.
I then measured the voltage at the + solenoid coil terminal and get +12V during start attempt. I then measured DC current coming from the +12V solenoid coil terminal --- there I only get 0.5-0.8A, I would expect about 3A to fully engage that solenoid. thus I suspect resistance inline with the solenoid coil + wire.
Relay (5) is closing or the solenoid wouldn't click and the mower wouldn't run when starter jumped. Since relay (5) is closing I conclude the brake switch, motion lever switches, and PTO switch are all fine since they control realy (5).
That leaves the seat switch, diode, and key swtich. I tested the key switch and it works fine, and ohms fine. I have not yet ohmed the seat switch or diode, and those are the only 2 things left other than bad wires.
not sure if I'm missing anything else.
If you want to rule out the diode for your piece of mind, wire one in parallel externally using alligator clips.
Here is one I have used and which is readily available to a few $.
The design purpose and use of these "flyback" diodes varies amongst manufacturers.
Some use the diode to absorb high voltage electrical pulses when the magnetic field around a coil of wire suddenly collapses.
The starter solenoid is a large coil of wire not unlike half a transformer. Same for the electric clutch.
When the solenoid is energized, a magnetic field swells up over and outside the coils of wire of the solenoid.
When the power going to the solenoid stops, as when you release the ignition key, this expanded magnetic field collapses around the coils of wire.
This produces a high voltage called back emf for electromotive force.
It is a high voltage and can move back through the wiring damaging other sensitive electrical devices like the coil of your relay.
Manufacturers are now taking steps to drain this damaging energy using a "Flyback Diode."
Below is a situation where Toro uses a diode.
John Deere makes extensive use of diodes to protect the machine from reverse booster or battery charger connection to the battery.
They use so many the group them in relay sized blocks as shown on the attached page.
The presence of a diode in a Kubota wiring diagram could mean many things. I have not found their manuals to offer much if any explanation.
Dave