I appreciate that you want the light to not blink and if that's what you want, there's no reason you shouldn't have that choice. Still, I can't find any "user selectable" option for it.
I will say that the miniscule amount of current the LED pulls and for the brief moment it's on, and on such an infrequent basis is so small that if that were the only thing drawing current that LED would probably blink for YEARS on one battery charge. In other words, I wouldn't worry about the power consumption but if the blinking is an undesirable visual disturbance, I hope you find a solution.