I don't think he did, I think its only open when people really need/ want it to be, he found the light and #s but didn't mention anything about falling in a hole.
I think another requirement in to go back in time for someone else, not for yourself. She wanted to help him fulfill his regrets rather than him fall in love with her. To be honest why would the light shine on 1 instead of the other #s I think its cause that's when she could help him change.
I love when people also analyze it deeply! And I love having a new point of view to consider while re-reading! thank you for your reply! ლ(´ڡ`ლ)
about the 3rd story: if the boy also fell in the hole, he also had a past experience. I wonder if he saw the number 1 too and traveled back 1 year or if it was another number. If it was number 1 and he went 1 year back, why wasn't anything written in the diary? and this time travel thing is too complex, it can't be written without considering the paradoxes.