[Big81Bronco]

I'm sure someone may disagree with this, but from my understanding the clicking sound is simply... Metal components in the driveline are cooling and contracting thus making the noises you are hearing and are normal.

 

[Big81Bronco]

It could be solenoids firing on and off for some unknown reason. Loosen the Neg cable from the battery get the truck to start doing it then remove the Neg cable and if it quits then you know theres a short in the system. Do you have a check engine light on? And maybe not be a **** to those trying to help you.
"The truck starts right up, runs fine, but as soon as I turn it off and get out I can here the click. I'm not sure if it's doing it while I'm driving" is what you said! Maybe be more specific with what you say. Want me to word it for you?
After the truck sits overnight I turn the key to ON and then I hear some clicking noises from underneth. Does anyone know what this could be? BOOM Done!! You're welcome!!

 

[Big81Bronco]

The only thing I can think to do ( AND PLEASE SOMEONE STOP ME IF THIS IS BAD) is while the clicking sound is happening, one by one remove fuses and or relays until it stops. You have a 04 RC so its a stick and shouldn't have any solenoids in the tranny so what I thought originally is useless. But please someone chime in if that's a bad idea. Just don't yank them all out at the same time

 

[Big81Bronco]

humor me. How does something with no moving parts make noise? Then he could can try disconnecting the battery froom the truck but hook up charger to it and check results.

 

[Big81Bronco]

No, I meant hook up the tender to the battery and check for noises. I don't think the battery is the culprit, but others aren't convinced. He'd need a jump starter for the other test.