The gear version of the
L3400 doesn't have a clutch switch, just a micro-switch on the range select lever. If you can jump the terminal and it starts then the starter is fine, if there's no power going to the starter solenoid then it's likely the starter relay.
I just checked mine, if any of the microswitches are not made you won't get the "click" from the fuel solenoid. For example, PTO engaged, no click. Range lever not in neutral, no click. Seat switch has no effect on starting, you can start mine from the ground, in the seat, or with the seat flipped up. However, the range lever has to be in neutral, which I think bypasses the seat switch.
The left most relay in your first picture is the starter relay. The picture I attached is not clear as a print, but they do indicate the left relay as being the starter relay. Where the "c" trails away in the text should read "check for continuity between terminal 1 and 3".
The following is the testing procedure according to Kubota WSM
1. Open the panel board and remove the starter relay.
2. Apply battery voltage between terminal 2 and 4, and check for
continuity between terminal 1 and 3.
3. If 0 ohm is not indicated, renew the starter relay.
Working back from that, one wire going to either pin 2 or 4 should be hot when the switch is turned to start with all safety switches made, the other should go to ground. If you have no power to the relay, it might be either the switch or the wiring between the two components. One wire going to either pin 1 or 3 should be hot all the time the key is on to provide a source for the starter solenoid, unless the safety system removes power before that point. I'd think it would interrupt power to the trigger side of the relay, not the main supply to it.
Sean