A NOCO Genius from Amazon is about all you really need. 1A or 2A is perfectly fine for keeping your battery in good condition over days/weeks, but you can keep in connected 24x7x365 if you want. They do sell a 2A version that is an on-board/direct mount unit (so all you need to do is connect...
You don't need to cover the entire screen. You don't touch 2/3 of the left side. Save yourself some cash and buy this one.
Pics of it installed in my DH here.
Spigen Tempered Glass Screen Protector [GlasTR Slim] designed for Ford Mustang (2024) 13.2 inch Dashboard Touchscreen - Crystal...
Mine light up for a period of time after you lock it, then they go out. Don't recall how long. And, yes, they are very dim, so hard to see in the daylight.
No, it means it's far less likely that the same person put something in one place but not another, and more likely that it happens when 2+ people are doing it.