Weird Clicking Driver Side Dash

I have a 96 1500 and i got into my truck yesterday and heard a rapid click noise as I got in and when I closed the door it became much faster like a fuse or rely clicking. I can feel vibrations underneath the panel that is below the steering wheel but couldn't find out exactly where it's coming from.The battery was also dead (brand new battery about 2 weeks old) This was right before work so I didn't have time to look at it but I charged up the battery and started it and turned it off and back on to make sure it wont crank over which it did


I got home Tonight from work and went to see if it was dead and sure enough, it was and still clicking. I noticed that using any kind of voltage (opening the door, using the power locks, turning the key into on, pressing brake etc) would stop it for as long as I was doing whatever draws voltage then would come right back on clicking and clicking. Jumped it off my jeep again and the clicking goes away as soon as voltage is steady. Once I turned on the jeep and the battery meter on the truck went up, the clicking stopped, didn't do it while the truck was running or for a few minutes after I turned it off. I disconnected the battery so I don't F it up and called it a night cause I didn't feel like messing with it.

Truck never did this until yesterday. The only thing I can think of that I did to mess it up was I had the battery disconnected for about an hour the night before to change out the door speakers so the battery didn't die from the courtesy lights. Any suggestions before I get out there to look at it tomorrow?

Edit: it's also worth mentioning that my turn signal fuse is always blowing and my passenger side tail light does not work at all. Not turn signal, brake, or running lights. I replaced the circuit board in the tail light assembly but that did not fix it.

Could be the flasher relay module that failed.
Seems like there's been a string of them failing recently.
Quick way to tell would to be to pull the module and see if that stops the clicking.
However it be a symptom rather than the cause.

Non GM flasher modules are like $10 on amazon under EP29.

OEM Part and interchange numbers:
GM 11516051, Standard Motor EFL6, TRIDON / NOVITA EP29, WVE 1R2190

Just to clarify, are you running LED bulbs or good-ol' filaments?

Just whatever comes stock really. Where and how do I check the flash relay module?

Mine started clicking while I was driving on the highway. It came from the dash but never figured out what it was. Clicking stopped eventually after a day or 2.