The 04 safety switch does have an 18g wire and it interrupts the signal to the trigger side of the relay, big wire not needed.
If you're gonna run the power wire from the battery/ignition thru that purple wire, then thru the PRDL of the trans, then don't use that 18g wire, too small.
Maybe have that 18g wire trigger a relay, then power the starter using those purple wires.