Yes, I simply used the power supply to verify the driver/ led combo (in the pill assembly) was able to meet the max output specs within the battery’s voltage range. That verified they can hit higher brightness levels at 4.1V .
I have used a piece of short heavy wire to bypass the tail cap (without a clamp meter), but when you’ve only got the tiny body barrel lip width (that is not anodised) to make the electrical connection. It’s not the best set up.
I’ll try some more testing though to isolate what’s going on.
Found the details here GFS16 - Battery Indicator Tailcap Light & 1mR FET Tailswitch! (Rev B) . Pity it’s not more readily available/ sold fully assembled. I guess the price would put most people off.