What color of light? White, red, green......
Some batteries can not hold a charge for a year with out a load. So there is that problem.
Here is a curve on the first battery I picked.
At 10mA of LED current, we have 800 hours of life.
At 3mA, we have 4000 hours or about 1/2 year.
At 1.5mA, the batter should last about the 1 year you want.
View attachment 98874
LT-5920 8.5Ah, 3.6V
So the real questions are:
Is this battery too large?
How much current do you need? (get a LED and try it)
There are other things to think about but this is a good starting point.
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Can we turn off the LED at night and save power?
Rechargeable battery?