Neither of them vs. none of them

[Jupiter]

Hi teachers,

Please look at this sentence.

Both Anna and Mary were too tired to walk any farther, but ..............of them would stop to take a rest.

1/ neither
2/ none

Which one is the correct answer? And why?

Thanks in advance

Jupiter

[Conchita]

Why don't you try to answer yourself first, Jupiter?

A little hint: the sentence refers to two people.

[Jupiter]

Hi Conchita,

Welcome back to the site. I haven't seen your post for weeks. How's everything?

Ok, with your little clue I would choose neither.

Neither of them would stop means both of the didn't stop.
How about none of them? Does it mean no one stopped?

Waiting for your explanation

Jupiter

[Rosalisa]

Hi

I think "neither of", which talks about "two choices of people/things".

None of means choices of more than two people/things?

Could you please tell what you think about my answers?
Thanks in advance.
Rosalisa.
_________________
If you want to change the world, be one of the change.

[Conchita]

In both cases, no one stopped. Rosalisa has given a good explanation to illustrate the difference:

neither means not either of two things or persons.