Back "translation" to the (historical) present tense: John says goodbye to his mother.
He will never see her again.

Ah, but we want the past tense. So, we write:

John said goodbye to his mother. He would never see her again.

Here, the past tense of will is would.

[MacMillan Dictionary][1]

In some cases would can be used as the past tense of will, for example, in indirect speech introduced by a verb in the past tense: I promised that I would visit her the next day.

That is the past tense of: He promises that he will visit her one day.

Some linguists like to just call this particular usage a modal. I don't.

[1]: https://www.macmillandictionary.com/us/dictionary/american/would#:~:text=Would%20has%20no%20tenses%2C%20no,she%20did%20not%20buy%20it).

Back "translation" to the (historical) present tense: John says goodbye to his mother.
He will never see her again.

Ah, but we want the past tense. So, we write:

John said goodbye to his mother. He would never see her again.

Here, the past tense of will is would.

MacMillan Dictionary

In some cases would can be used as the past tense of will, for example, in indirect speech introduced by a verb in the past tense: I promised that I would visit her the next day.

That is the past tense of: He promises that he will visit her one day.

Some linguists like to just call this particular usage a modal. I don't.