Here is the wiring in that fuel shut-off interlock area:
...You need to take this in conjunction with the starting safety wiring because of continuation from the K1 Neutral Start Relay on wire #810 -- here is "the rest of the story." Wire #810 and #811 are both connected together at the coil terminal of the relay, even though neither of these two wiring 'excerpts' shows that.
I can't explain why the rear PTO switch does not cause the engine to stop at the present time...it should if the ground speed and front switch do. The fact that the ground speed moving out of neutral causes the engine to stop would indicate that the F2 10 amp fuse is blown, that fuse-holder is not making contact, the seat switch is bad, or the wiring is shorted or cut.
Since you did not mention releasing the brake pedal also causing an engine shutdown, I presume that your tractor is below SN 596,723 when this switch was not yet fitted.