What situation do you use ‘if I need persuading’ in?

Question

I can understand need persuading virtually means need to be persuaded, but once it’s implanted in a sentence as the form of “if I need persuading”, I can’t figure out what the speaker is saying.

In the following citation, it seems that Harry doesn’t conclude his sentence after if I need persuading. Because of this, I can understand even less. So I tried searching for other examples on the Net, but I could find few examples and it’s difficult for me to understand their meanings clearly. I’d be happy if you could help me.

(Harry and Myrtle are hearing a chorus of a magical egg and trying to solve the mystery of the lyrics. Harry has to be under water when he hears the song.) (the egg’s song)

"Come seek us where our voices sound,

We cannot sing above the ground,

And while you're searching, ponder this:

We've taken what you'll sorely miss,

An hour long you'll have to look,

And recover what we took,

But past an hour - the prospect's black

Too late, it's gone, it won't come back."

”Hear it?” said Myrtle. ”Yeah… ‘Come seek us where our voices sound …’ and if I need persuading … hang on, I need to listen again….” (He sank back again in the water.)(Harry Potter 4 [US Version]: p.463)

I have no idea. What is he trying to say?

(From Google search)

Q: How can I persuade my mum to get me a dog?

A: If your mom needs persuading she does not want a dog. I am a mom of 4 children and 2 dogs and if I need persuading over anything the answer is ‘I don't want it’.

I feel it roughly means 'absolutely'. The same goes for 'if your mom needs persuading', I suppose. 'Need' might mean 'strongly want' and the mother has a strong desire to get her son a dog (she wants to be persuaded by her son) but the situation prevents it completely.

EDIT: adding the egg’s song to the citation.

Answer 1

You’re right in thinking that needs persuading means much the same as needs to be persuaded, although the two might be used in different contexts. If someone needs persuading, it means that they are not necessarily opposed to a course of action, but need to be shown the advantages of taking it. It’s the same construction as, among others, needs encouraging, needs consoling and needs mending.

Answer 2

It could show his reluctance to "Come seek us out", given his first experience with the dragons. They are asking him to seek them out and he's asking them, "why exactly would I do that?"

Or it could be a typo. Perhaps it should be, "as if I need persuading", referring to the same line, meaning, they don't need to tell him to seek them out, he knows he has to do it anyway.

On the second point, there are levels of needing persuasion. I might be opposed and would need significant alteration of my position to acquiesce, or I might be indifferent, and am only looking for compensation. I could be persuaded to give you the information if you gave me your watch.