Is it normal that my neighbors daughter calls me a second father?

It's completely normal, and it used to be much more common.

Sounds like you have built an awesome relationship... that will last your lifetime if you continue to nurture it.

It takes a village to raise a child. You're clearly a contributing member of her village.

Most parents will have no problem with this. They like it when their children have other people to talk to and do things with that are decent people (even if your values are somewhat different).

It's not normal in the sense that it's common, but as long as her parents and your family are cool with it, I don't see what's wrong with it. It's good for both boys and girls to have a positive relationship with at least one adult male role-model when they're growing up. It helps boys to learn what it means to be a man, and girls to learn what sort of caring, respectful behaviour they should expect from the men they choose to become involved with later in their lives.

However, I'd suggest that you be very careful to never call yourself by that title though. I suspect that could easily result in her real father feeling guilty that he hasn't been able to spend more time with her.

Sounds like you guys have a cool relationship. Must be a good dude.