Well I finally got around to connecting the circuit light and pulling fuses. Good news: I found the circuit with the power drain as the light only went out when this fuse was pulled. The fuse is identified as PWR ACCY which I am assuming means power accessories. Bad news: under the usage section it lists this fuse as controlling parking lamp relay, hatch release relay, power mirror switch, radio, shock sensor (don't know what that means), and instrument cluster. I will be taking the car into a shop I trust to have the correct circuit narrowed down to be the problem causer.
Any of you guys have any ideas as to which circuit that utilizes this fuse might be the problem?

I had a lot of 4th gens, never really had this problem, maybe look for a break in the wire?

Reading this made me think about my 02 car so I went to the shop to try it. I haven’t driven it for about 4 weeks, hit the key and it fired right up. A bought a new AC Delco battery for it in June 21. No issues with the battery
Dana you’ve got a problem with that circuit and it can be fixed. Going to take some time n effort but you can fix it.
Good luck,

First you need to get a wiring diagram to see what is serviced by this circuit (fuse). Vanity mirror visor lights, glove box lights, trunk lights, console lights, and under the hood lights are notorious for draws in any car. If all these are on this circuit, just disconnect each one at a time to see which is causing the draw and makes the test light go out when you do that. Good luck with your quest to see what's killing your battery. If you were closer to Chicago, I'd have one of my Technicians take a look at it for free. Keep us posted. Inquiring minds want to know.

Bill

Well after having the car in a local auto repair shop for 2 days they could not find where there was a battery drain. They charged the battery and told me that it was their opinion that the problem was either with the battery not holding a full charge anymore or with the ignition switch in the steering column.
I have been checking the battery charge and it has never been below 12.0 volts and today was 12.5 after the car has sat for a few days. It does appear that there is no longer a drain or at least no longer enough of a drain to weaken the battery.
I am going to keep my eye on things and if they revert to like they were before look into getting a new battery and maybe taking my car to another shop. I did purchase a battery cut off switch but haven't installed it yet due to the car behaving normal lately.

I had a 1999 Z/28 for almost 20 years. I bought it in 2001 bone stock with 17k miles on it and never did any electrical system modifications to it. If it sat for extended periods of time it would do the same thing. I put a quick disconnect on the battery and never had issues again after that. I tried several types of batteries, none really made a difference prior to the disconnect. My guess is the security system on the car when locked drew enough power to drain the battery after sitting for a week or two.

Hmmm, I wonder if the security system could be my problem too. I haven't been locking it while it is sitting in my garage, and it seems like the battery drain has been reduced or eliminated since I stopped locking it.
I bought the car new and am just dumbfounded as to why this problem only showed up sometime in 2019 after 17 years of no starting problems.

It has been my experience that a drain in the radio circuit is the radio. Is there a CD in it now? The drain can be a switch internally sensing and causing the drain.

Get a battery tender and leave it hooked up whenever you're not driving the car. The battery tender will keep the battery fully charged to it's optimum capacity and make your battery last a lot longer. I have a 97 30th Anniv Camaro and that's what I do...I don't drive the car that often particularly here in Chicago during the winter months so the battery tender is always hooked up. It is so sensitive that if you open the door and the dome light comes on the battery tender goes right into the charging mode and take the battery back to optimum charge. Hook up a battery tender and forget about it and your problem will be solved.

No, there is no CD in the player now. There is no light on right at the entrance to where a CD is inserted.