As previously posted, H and I are currently installing the backsplash. I have light rail molding at the bottom of my cabinets and right now there is about a 1/4 inch gap between the top of the backsplash and the bottom of the cabinet. You can't see it unless you actually duck under the cabinet. I say that H needs to cut slivers of tile to cover the gap...he says since you can't see it unless you bend under to look (or sit on the floor) it's unnecessary? Who's right?
I say your H. If you can't even see it unless you duck down to look for it, I wouldn't worry about it. Cutting all those 1/4" slivers (and putting them in place!) is going to be a nightmare.
I would leave it, if you ever need to do anything to the lights you don't want to have chip away at tile to remove them. This way you have a little space for tools.
Okay, so I measured the gap. It's actually just shy of 1/2 inch, but no, you cannot see it unless you duck under. Even sitting at the table, the backsplash extends up high enough that you don't see it. Under the cabinet, it's like this
Leave it of fill it? I think 1/2 inch would be too thick to caulk?
Leave it. No one will notice or care. Cutting that thin of slices on a cheap wet saw accurately will be very frustrating because the slide and blade flexes a lot. If you just have a tile snapper forget it.
I wouldn't try to caulk it either because that is a big gap and it would make removing the upper cabinets later difficult. Caulking that big of span will look strange and it will be hard to get that perfectly smooth. Your tile has a rounded edge so it looks like a bullnose edging which makes it feel intentional if anyone ever did see it.