PNP Transistor Not Working as Expected with Higher Voltage

So I think I am just going to bite the bullet and amend my PCB design. I tested this design last night but welcome all feedback. Making this an appropriate high side switch with a 20K resistor on the gate and 1k as a pull-up seems to work.

Any insight would be greatly appreciated

Try adding a 10 volt zener diode (rough and ready level shifter) like this: -

use a FET instead. a p-channel depeltion MOSFET or JFET will turn off when it sees 10V on the gate, and turn on for a low voltage there.

^{simulate this circuit – Schematic created using CircuitLab}

Even an NPN would always be only with 1K to 10K to 15V. Maybe 33K is OK or no 10k pull-up needed if using logic levels. REF

Summary:

1. Change PNP to NPN
2. Remove 10K for any logic level 1V to 5V ON.
3. Invert output in software if possible.
4. Define input signal & state when ON/OFF with Voltage and Z. Let Ic/Ib=20 roughly.

The left side works. Right side (no Good) PNP will always be ON.

Your issue is that you have Q1 configured as an emitter follower. So the voltage on the emitter will be about 0.7V higher than the voltage on the base.

With your 12V adapter, when the charge ends you didn't have enough voltage across the diode to turn it on.

With the 15V adapter you'll have about 10.5V on the base when charging is done, and 11.2V on the emitter. If your diode drop is say 2V you will have 15-2-11.2 = 1.8V across R1, and 1.8mA in the diode. Probably enough that it still glows.

No easy solution by changing the transistor, you'll have the same result. It has nothing to do with breakdown.

If you don't want to change your PCB you could try a bigger resistor for R1. Increase it until the LED no longer glows and see if you get acceptable brightness during charging.

The better approach would be to use the transistor as a switch, but that's a PCB layout change or lots of cuts and jumpers. JRE's suggestion of putting some LEDs in series would also work.