It’s not easily customizable.
When the banner appears also depends on some engagement checks made by the browser, so in recent history, it would not show on the first visit from a new browser.
When the browser signs us that the install prompt is possible, and we detect that the user is at least trust level 1 we show it.
Trust level 1 in Discourse is a very quick thing to obtain, and it helps us so we don’t spam people who just arrived with annoying banners.