PNP high side switch base current leak?
A red LED will glow visibly with really tiny currents. Maybe as low as 10uA or 100uA. I don't fully understand your explanation of your circuit. But I suspect that when the LED is on faintly, it is because a small amount of base current is able to flow, most likely to !PI_RST, but it could even be reverse current in the diode, D2. This base current is amplified by the transistor Beta.

The solution is two steps:

First, find out how much current is flowing through the LED. Do this by measuring the voltage across R1 when the LED is glowing faintly. It will probably be mV, but of course I am not sure. Anyway, calculate the current through the resistor and LED using Ohm's law. Assuming it is a small value (less than 1mA), go to step 2.

Step 2: Put a resistor in parallel with the red LED. The resistor should be calculated as follows:
V/I = R
Where V is 0.2 * Vf for the LED, and I is the measured current. The idea is to provide an alternate path for the small current so that it doesn't go through the LED. As long as the current going through the parallel resistor does not cause the voltage to rise to near Vf of the LED, the LED will not glow at all.

If the resistor works out to be a small resistor value, then this solution won't work. But if it works out to be like 10k or 100k or more, it might be an acceptable solution.

Good luck! By the way, increasing the base current resistor might help. Just make sure you don't increase it so much that the LED doesn't turn on brightly when it is supposed to.