Long lived LED indicator
Do the math.

A LiSOCl2 AA size battery has a capacity of 2400 mAH. A 1mA LED current is equivalent to 8760mAH per year, so your duty-cycle must be lower than 28%. Take 10% to be on the safe side and leave some current for the timing circuit. That means your LED draws an average of 100uA. A simple micro-controller can be made to draw much less (&lt; 1uA).

uint128_t quotes 500mAH cacacity for a 9V block. That's around 1/5 of the LiSOCL2 I would choose, so for the same 1mA the duty-cycle must be ~ 2%. Or take a low-current LED. Test it: is it bright enough for you at 0.1mA?

Did you measure the average current drawn by your C555 circuit? According to the datasheet ~ 0.5mA must be attainable.