If the GP relay doesn't click, it is either the relay itself or a bad connection someplace between the Relay and the key switch, or possibly even the key switch itself. This clicking has nothing to do with the fuse in the relay.
With the key turned to the glow position, try removing and reconnecting the small connector on the Relay 5 to 10 times and listen for the relay to click. This solved my GP not working problem because there was corrosion on the contacts between the relay and the connector.
If the above doesn't work, before replacing the relay, I would determine if it is getting voltage when the key is turned. If not getting voltage, a new relay will not solve your problem.
P E H