My boss is going to go to a long time vacation, I want to ask him to inform me if during his vacation I should consider on some daily task, what should I say?
That's a good idea and something your boss should appreciate. What you proposed is just fine. If I were in your shoes* I would just ask him before he leaves if there is anything you can focus on while you're gone.
I had this happen a couple of times at my former job and my boss was always happy to provide input. I think it let him know that the ship wasn't sinking while he is on vacation. It really helped him detach from work and truly enjoy his vacation. It may do the same in your situation. You should go for it and just ask him.
Your boss's email or outlook should have an auto-reply or "Out of office message" which will specify on possible ways to reach him (or the lack thereof) during vacation. Based on whether he is completely offline or checking emails - i.e. "limited access to email - you should communicate appropriately.
Usually some news is better than none at all. In fact, it is good to know in advance before anyone leaves on vacation to clarify on how to reach them because the auto-reply can be a cookie cutter.
Edit: initially commented, but decided to add as answer (although @Matt G. 's answer was picked already)