If the user is closing the keyboard by exiting a field after entry, you can use either the OnObjectExit (tied to an object) or OnRecordCommit (tied to the layout) script triggers. However since the keyboard is controlled (mostly) by iOS and not by FMGo, I do not believe there is any action tied to the keyboard itself closing.
What exactly is your goal?
The main goal is to commit the record so the "Previous" and "Next" buttons disappear.
I would say using the OnRecordCommit layout script trigger would work for you then. You can use a commit record script step, followed by a go to object script step to go to a non-entry object (eg a text header).
The "previous/next" buttons on the iOS keyboard are tied to the tab order of your layout. Since they are in the iOS keyboard itself, I don't believe you can control their display. I am not sure but I think you could maybe disable them by removing all tab orders from your layout completely.