iPod Touch 2nd Generation (Used) boots into Apple Logo when dead, then shuts off. If charged however, everything is normal. What is going on? I've been trying to calibrate my battery after enabling the battery meter by editing a .plist file in a copy of my iPod's backup. I restored that backup to my iPod, and the battery meter worked just fine. The iPod is running iOS 4.2.1.

However, attempts at calibrating it do not work. It will shut off after reaching "0%", but if I hold the power button, it just boots back into iOS with ~19% remaining. 

I let it drain after that, and if I hold the power button again after it shuts off, guess what? It's back at ~19%.

I repeat this one more time before it refuses to boot into iOS. Once it drains the third time, it will boot into the Apple logo, then shut off after ~15 seconds. If I continue attempts to boot, it will continue doing this.

If I plug it into a charger though, it will boot into iOS and claim that it has 3% remaining and is charging. There are absolutely no problems with it (besides the weird battery meter).

I also own an iPhone 5 (iOS 10.3.2), and when that device hits 0, it stays there. It will not boot up and just shows the "I need to be charged" indicator.

I'd like to know what's going on here, how to get the battery calibrated correctly, and how to get the battery as stable as possible (Similar to my iPhone 5).

This is the method I used to enable the battery percentage meter.
"You do realize this device is almost 10 years old, and that the battery is probably showing its age? I suspect that any amount of calibration you attempt isn't going to make much of a difference and will continue to present you with perplexing results." - IconDaemon

"The firmware in the 2nd generation might not be as advanced as what's found in the iPhone 5. In addition, the 2nd Gen Touch can only take iOS 4.2.1. Perhaps a combo of these two things, in conjunction with an old/failing battery, may be causing this anomaly. I don't think you'll get a satisfactory conclusion to your quest -- it may simply be an unusual set of circumstances that is leading to what you are seeing. Lastly - it doesn't seem as if the 2nd Gen is malfunctioning in any other way. In the immortal words of Lennon/McCartney - Let it Be." - IconDaemon

The battery meter will display unpredictable fluctuations in the percentage due to the battery being very old, causing the device firmware to be unable to accurately measure the percentage remaining.