There was a little clunk as I was driving down my road so when I parked the truck for the night I climbed under it to tighten a shock mount bolt. While I was under it I heard this... next to the rear prop shaft/transfer case. Like a constant running sound?

 

That video is no help, better do a better job describing the noise if you want some help.

 

How is the video no help, did you watch it? Turn the volume up, you can hear the sound, it's like a buzzing. The video is showing what the part is, and the sound it is making.

 

Do you have SLS (self leveling suspension), aka. air bags on your rear shocks? That could be the compressor running.

 

i have to agree with DM, i cant tell if your in the rear or the middle of the truck.
if it in the rear could it be the fuel pump? if your in the middle; did your truck have sls that was converted and it is the compressor? if all else fails pull each fuse one by one until it shut down, then track that curcuit.

 

I mentioned in my post that it was right next to the transfer case. I don't believe it had SLS, I somehow doubt it.

 

next to the transfer case in a black plastic box?

 

Yeah, after checking out microcat for a bit I'm thinking it may be wtb000090 part of the secondary air system/fuel system?

 

Does it continuously run or just for a short time?

 

For at least a few minutes after I shut it down last night, though I've never heard it before. I only heard it last night because I was under it.