Seems a Death Note would need your name exactly as printed on your birth certificate, so if I wanted to kill someone with one, for example "Kaitelynn Woods", it would not work if i wrote it as "Kaitlyn Woods" even if I had her face in mind and everything else was in order. So for Light you'd need the kanji symbols, and you'd also need to spell his first name as Tsuki as it shows on his birth certificate.
Also, trying multiple times is a no no, as if you misspell a name on accident more than 3 times, the person you were trying to kill can no longer be killed with that Death Note. Ofc it only works if it's accidental, you can't protect someone with this method, it's only a rule to keep you from just guessing till you get it.