There's no such thing as a definition of a hodler. It's just a made up term, based on unintentional drunken joke.
Hodling is just a meme for not selling. It's has nothing to do with the concept of non-custodial or custodial wallet. Back in 2013, owning your keys was pretty much a standard way to own your coins, as CEXes were much more unreliable then now. They were constantly exit scamming or blamed hacking for exit scamming.
HODL is just a slang that means buy and hold something for indefinitely. It doesn't directly have anything to do with the concept of custodial or non-custodial but at the same time, it does when it comes to Bitcoin. You are not a HODLer, i.e. someone who holds Bitcoin when you own them on an exchange and I think we all agree with that. How can you say that you hold Bitcoins when they are on exchange? On exchange, you just see numbers, you have no other control over them. If the exchange wants, they can block you or change those
numbers that you see the way they wish. When you deposit money in bank, you don't own the money anymore, you only own it when its in your pocket and even in this case, the government can make it go bankrupt anytime they wish.
You can only say
I hold(or HODL) Bitcoin when you control the wallet, that's all what I wanted to say.