"information gap" here just means that you're introducing new/unknown information with the が particle. You can't use は when the other person doesn't know what you're talking about.
What は does is it puts focus on something, assuming it's already in our shared knowledge/context.
Yeah me too. Even after going as far as reading research article, I still don't accept that kind of explanation.
"Information gap" just mean that you didn't talk about that before. So you're "filling" the missing information with が (which is supposed to be the subject). Never made any sense to me since when you introduce the "topic", you're also adding information to the conversation... So your question become "what is the difference between a subject and a topic?". Good luck with that. I completly gave up on all those kind of explanation and I'm only studying gramar in japanese because of those (Japanese grammar isn't perfect either but it makes more sense for me at least).
Honest advice, take the explanation that makes senses for you. And if they doesn't, just ignore it. You can always learn it later with immersion. And it's sometimes easier too. I understood a lot of those explanation later by hearing natural japanese first (instead of artificially make japanese fit into those theorical box). And even if I don't like those kind of explanation, they still make some kind of sense. So don't block yourself on that. Time (and immersion) are sometime the answer in those cases
