The resistor simply allows K-10 to put the resistor in series with the fan circuit for the LOW speed [ a/c high pressure circuit]
This R is behind the drivers headlamp.
You can exchange the relay for the test of the High speed [ K-9] circuit.
You have to have a relay/ relay coil circuit fault because you stated the fan ran when jumpered 30/87.
And you know you have relay coil feed for both K-10 and K-9,
cuz they are the same fuse [7]. So the completion of the circuit is a switched ground [ This is what the ETC does].
My guess is open relay coil or coil pulling contacts in, but load contacts are burnt to point of non conduction.....