We don't get the best info on the chassis side of the wiring, so a bit of guessing is needed!
Bear with me a bit and see if we can get close?
I need to ask some questions to get on the right level to explain what I think might have happened.
Are you familiar with the way a starter solenoid works on cars or the generator? They are much the same idea but different shape. Does your starter solenoid in the genset have two small wires that act as controls for closing the solenoid contacts and then there is one big battery cable that brings 12Volt in and it is passed on through to the starter motor when the contacts close?
When you say you have 12volts at the solenoid, I'm guessing you mean on the big cable? That would seem to be the cable bringing power to move the starter motor.
But when you say you hear nothing like the solenoid moving? Those solenoids are what you may have heard on cars as a click, click, click, when the car won't start?
I think you should also hear some sort of click, even if lower, when the solenoid moves to close the contacts.
I think there will be two sets of wires at the solenoid. The big one from the cable but also the small control wires from the switch to tell it to stop or start.
I feel you are missing that control signal to tell the solenoid to move and close the big contacts inside!
But part of the trouble is that we don't get much good info on the chassis wiring and we have to sort of feel our way along.
Can you spot a connection/plug that might fit this drawing and wires?
Click these snips to get a better view!
It shows in the generator compartment but no idea if on top, side, or where!
If you can find the three green wires and one purple, that is likely to be the right plug.
Winnebago does label the small wires to help ID them, so you may find this helps.
We also have this chart to "decode" the ID!
What I would want to check is that you are getting the signal passed from the start/stop switch inside and down to the control wires at the solenoid?
I can't trace it back far enough nor get a good idea from the idea but I "feel" wire LL should bring ground down to this plug when you push the start switch! Possible it could be battery however as I don't get a lot of the chassis wiring to tell for sure!
Check first for battery showing up there if you can find it when somebody pushes the switch. Then if not seeing battery show, check for it being ground sent in. Check first for battery to avoid blowing a fuse in the meter???
Bottom line is that I think you are not getting the start signal sent to make the solenoid close to make the starter turn!
If solenoid is not moving, that will be first step to getting the starter to move!