[ViperDad]

I'm also thinking it's a relay or battery trickle charger or something else electrical. My '06 QC sits quietly when it's resting cold so I can't think of anything else it could be. You could try disconnecting the negative battery terminal and jumping it with a meter just to see what kind of amperage/voltage it's pulling.

 

[ViperDad]

Dangit, I thought you had solved the mystery! Maybe you just have a bad cell in your battery?

 

[ViperDad]

Call me crazy, but battery charger connected = clicking but with a working truck. Battery charger disconnected = no clicking and dead truck. Sounds like a battery issue to me.