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Need to make very loooong lasting battery operated Mini LED light for backlit painting

For some of you brainiacs Im sure this will seem like an incredibly easy project but for me, Not my area do expertise in the least.
I need to make a simple machine for part of an art project. I need to have two small LED lights placed one each on the tip of two  clock hands . I need the lit clock hands to be battery operated ( looong as possible) and flattish ( maybe an inch in depth at most for entire piece) so it can hide behind a painting. Would like it to  operate lit up and moving in clockwise circle nonstop day and night for at least a year .

Any ideas? 
What # volt? How to make simple clock ( besides just buying a kit? It only needs a very long hour hand with bulbs on each end ( say 12 oclock and 6 oclock) Where to get small ( 1/8 to 1/4" diameter)  long lasting LED bulbs? As I said before, I am an absolute amateur here! 

Thank you.
Maggie