I'm working on a 2002 Tiburon GT with the v6 and manual transmission.
It won't crank over at all except on random occasions where it starts up fine one time then won't start again for quite a while.
I've checked the relays and all of them are closing like they should. The clutch position switch closes when the pedal is pressed in.
I didn't have it where I could lift it up to check the wire leading to the starter solenoid, but I suspect that wire is the problem.
Am I on the right track? Is there a fusible link in that wire?

 

Check the switch itself first. Just because it closes physically doesn't mean the connection internally is working.

 

Perhaps I should be more specific... When I say the switch closed, I mean electrically. Less than 1 ohm resistance measured by the multi-meter.

Oddly enough, it is just now starting up multiple times during the same trip.