That’s strange, I would have expected a simple bleeder resistor on the driver to solve any weird behavior.
I use lighted tailcaps all the time in my lights, usually with a nanjg105c driver (similar to what most Convoys have). I just stretch a 750 or 840 Ohm resistor between the first star (technically just a ground pad) and the spring. And for firmware, I use my own which has it’s roots in Biscotti… they should act the same in this regard.
Pic here: D.I.Y. Illuminated tailcap - #1748 by gchart
If your driver is the style without stars, you just need to place the bleeder somewhere between ground and positive. Perhaps by stacking on top of the decoupling capacitor.