Batteries can be a tricky business. There is the obvious capacity question a it will diminish with use because of the internal chemistry.
However, this internal chemistry change can impact another important point: the stability of the voltage provided. I had a tablet battery that would start going crazy under 40% if used a bit much because the battery was not providing a steady voltage and it was either glitching, freezing or shutting down.
On a Mac, you may have it shutdown just because whatever is in the battery is not sufficient to keep running (but does it powers off or does it goes to forced sleep like when reaching 2%?).
You can check the stats of your battery (cycles, current capacity vs original) through software but that will not change its state (do not have a ref for 9 but know coconuBattery on X). The circuit with the light may tell you if all cells are maxed but if your battery only have 10% of its original capacity AND the charge/discharge is a chaotic mess, it won't do much good.
If you cannot find a Newertech battery, at least you can find comfort that chinese noname batteries are still available (not the most performant but better than nothing).