OK, took the battery to the local Walmart and they tested it, and believe it or not, it tested as good. Now I'm really not sure what's going on!
This is the test receipt (battery was purchased on 11/2019):

 

The clicking sound you hear could be possibly a relay closing and opening or maybe a circuit breaker doing the same thing.

What would help is if you or someone you know would go to where the clicking sound is loudest and attempt to narrow down the source and then go to the fuse /relay panel and verify if it is coming from there. Once you have some idea where it is originating then you might be able to find that area in your owner's manual in the specifications section that should show a picture of the fuse /relay panel. The info in there should help direct you to the circuit involved ,,,, IF it is actually a problem with one of the two suggested possibilities.

 

Clicking is coming from behind the dash, somewhere near the center (like around the radio area) and yes, it does sound like a relay of some sort. I have a friend who <claims> he's familiar with Chevys and their issues and will be coming over later today (5/4) to see if he can assist me with it.
My vehicles almost never correspond to "the book"; for example, "the book" claims my vehicle has a cabin air filter installed.......it doesn't.

 

OK, everyone - I/we (a friend who's familiar with Chevys) found out the problem.....
Apparently, there was a keyless entry/anti-theft module (I found out what it was by researching the FCC ID number on it) installed under the dash that I was unaware of when I bought the vehicle 4 years ago, from a private owner (they may have not known about it either) and it somehow malfunctioned and caused my "no start" condition; as soon as my friend, Dave removed it and rewired the leads going to it, everything returned to normal. Yes, I can still lock/unlock the truck with my fob, so that's not a problem.
Thanks for all the help and suggestions to everyone who answered me, anyhow!

 

Glad to see you and your friend got it fixed. Thanks for reporting back as it might help someone in the future.

 

The joys of buying previously enjoyed vehicles.

 

I have a 99 K1500 5.7L that is running great but under a load the battery light comes on and the volt meter drops to almost nothing. Always when it shifts down to first gear under a load.
Battery and alternator check fine. I've redone the ground connections to bare metal and added the Big 3 upgrade. I'm at a loss and getting frustrated. Anyone experience this? Any ideas? Thanks in advance.

 

If grounds are good, then the positive wire from the alternator would be suspect when it flexes from engine movement when under load.