Yes. I push the button and it’s high, the light will stay lit. Push the button again, a very rapid blink. Repeat this on this flashlight, until it has cycled back to the high function, when it will once again stay lit.
On a couple of the lights, I also get a low beam which stays on.
And it doesn’t appear to have anything to do with whether it’s a 5-mode light or a 3-mode light.
It’s kinda up to you how much you remove. You can strip the whole thing back so it’s a bare flat top cell if you like (leaving the original Panasonic wrapping on of course)
I still don’t understand how you end up with a strobe mode that pulls more current than a high mode, especially when the driver is regulated. In other words, why isn’t high tripping the protection too?
The only real concern is whether any of your flashlights are without a spring on the bottom of the driver board. If they don’t have one, flat tops are unsuitable. You also wont be able to reliably use flat tops in multi-cell lights, if you ever get any.
When you switch the light on/off, there's always an electrical spike. This can be very high current for a few microseconds, but relatively harmless since it's very short. These spikes are way higher current than running on high etc.
However in this case, the protection circuit in OP's battery is sort of overprotective, it saw this current and immediately shuts off, thinking it was a dead short.
And it’s funny in an odd sort of way, that this batch of batteries was probably stronger than they anticipated for, when they put the protection circuits in there.