I haven’t checked mine to be sure, but I assume if the light is on and hits the low voltage to trip LVP the driver goes to sleep or continues to check voltage to know when to wake back up. Either one I would think would be a very low power consumption. After LVP kicks and you turn the light off then the vampire lighted tail cap would kick in again.
To solve this defect, you would either need to change the lighted tail pcb out for something like gchart has done or change the current limiting resistors out to a higher value (something up in the 100k range) but the tail cap will be pretty dim then and only be seen when its dark (switch boot is not very transparent). Then there’s always the option of just removing any of the components that make up the lighted tail cap pcb (leds or resistors) but then you have no lighted tail cap.
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Maybe Yokiamy can answer the question on weither it blinks or shuts off with LVP. 