The red wire is fed by F8 rated at 10 amps. However it appears to be the main feed to the instrument cluster and everything connected to it. But yes, the blue is the switched lead which runs back to the connector X09 on the back side of the fuse panel. That connector has the blue switched wire and a black wire to ground in it. The diagram doesn't show the blue wire going back into the fuse panel. It just shows the connecter located behind it. I'm not sure what rating the solenoid has. It gives no further information.
My guess is they used a momentary switch to open a electrically operated valve to lift the mower hydraulically. When released, I'm betting the valve routes the hydraulic fluid back to the return side and allowed the mower to drop. I kinda like the idea. Again, just a guess...