This all started around 2 weeks ago when I went to replace the battery on my '79 SR5. The first one I got (different brand but correct amperage) made it loop/sputter at idle until it would completely die after a few minutes. After putting the old battery back in (24EXTJ), it fired up no problem and ran perfectly fine for a few days until I tried to start it about an hour after I got home from work, and got nothing. I figured it was a dead battery, so the next day I went out and got a new one, but was given a 24REXTJ (750 CCA 935 CA) instead of a 24EXTJ (700 CCA 875 CA). I didn't realize till I was going to connect it and saw the reversed terminals. I figured it should be fine as long as I connected to the correct terminals, since it was just higher amperage. The same thing that happened before happened, so I swapped out the battery for the correct one, but when I was installing it, I accidentally bridged the connection for a split second but that didn't seem to damage anything. It fired up and ran well for about 10 minutes, then the same sputtering started happening again.
At this point, I figured that the battery wasn't causing my problems, so I moved on to the voltage regulator/alternator. I went out to order a new voltage regulator (which should be here on Tuesday), and when I got back, I tried to start my truck to move it to a better position, but only got a single click, nothing other than that, and the dash lights. Worried that I may have drained the battery, I hooked it up to a trickle charger so that once I got the part, I wouldn't have to worry about a possible dead battery. After letting it charge for a few days, I tried to start it one last time and got the same singular click and dash lights. I did not notice that the voltage readout on the charger got up to 17 volts when I tried to start it that final time, which makes me think the voltage regulator is what I need.
I'm worried that something else is going on other than the voltage regulator, or that I fried some electronics from the multipull battery change attempts. Does this sound like a voltage regulator or a bad alternator to y'all? I've been waiting on parts for almost 2 weeks, so I've been second-guessing my diagnosis, so I would really appreciate some advice on this.

Other info:

All fuses looked good but I replaced the engine fuse just in case
Had the GM ignitor module fixed a few months ago
I have a video of the sputtering/looping at idle wasn't able to upload it

 

Before you do anything else, check and clean your grounds; especially your main negative to body battery cable. It sounds to me like your cable has a "memory", meaning... it likes the old battery because it has been in that shape for a long time and the connection point to the body is clear of corrosion at that exact contact point. When you switched batteries, the new terminal arrangement pulled the ground connection just enough out of it's old placement to cause high resistance, then a dead connection. When you put the old battery back in, the old connection point was re-established for a bit and was happy.

Take the bolt out and wire brush the bolt, terminal, and threads where it connects to the body. Might as well do the same for the frame and engine grounds while your at it. Hopefully that will get you going, then re-check the voltage regulator. If it's consistently 17V, then it's bad and will kill a battery.

Also, the Toyota Factory Service Manual has bench testing instructions for all electrical components. For the regulator, you take a set of Ohm readings across the different terminals to verify it's condition.

You are correct, a battery is a battery. As long as it is the correct voltage and has at least the minimum amount of amperage to crank; higher amperage, form factor, chemistry, or terminal arrangement doesn't matter. I have a tiny little lithium iron phosphate battery (LiFePO4) battery in my riding mower. It's about a 1/4 the size of the lead acid battery and 1/8 the weight, but is the correct voltage and much higher CCA.

 

Thanks for your assistance, I was able to get it fixed with the voltage regulator + cleaning up all of the corrosion. I'm fairly certain that both were playing a factor in it not running.