Not sure why you think a relay is needed all your doing is making it think the thermocoupler is open.
I just installed a toggle switch and a wire to each red wire by the thermocoupler and never had an issue, done several atv's as well along with hundreds of other king quad owners.
2010 Prowler XTZ 1000-
27" Grim Reaper Tires/Home Made Roof/Arctic Cat Mirror/Quadboss Folding Windshield w/ home made support bar/LED Tail-Brake lights//Venom 4000 lb Winch/Amsteel synthetic line/Home Made Doors/Custom Adjustable Seats/Custom Oh Crap bar for passenger/Tonneau Cover/Fat Max storage Box in bed
Tiger Tail Towing system