I would hang it horizontally and center it between the light and backsplash. You will have about 6-7" of wall space on all four sides of the mirror. I always find it helpful to draw the vanity, lights, and mirrors on graph paper.

It will be too narrow I'm afraid. Unless you decide to change the light fixture for a smaller one/put sconces on the side..

Any possibility to do a mock-up? Even if you draw it quickly on a piece of paper-will be helpful. Or put a tape on that wall just to see where the edges will be. Because it might look great horizontally but might look a bit awkward too. Depends on the frame, and how your light fixture goes, etc.

If it was something smaller I'd advise you to try it and return it if it doesn't work.But mirrors are heavy and, frankly, a pain..

I went through the same type of thing when I recently had our bathroom remodeled. We have a 40" vanity, 32" wide mirror and 26" wide light fixture which looks fine.

I think the light fixture you are thinking about will be too small.

As for having it hung horizontally--you may want to reconsider that. I think it makes a bathroom look dated. Look on Houzz for horizontal mirrors to get an idea.

Actually a narrow mirror the full length of the vanity is a very contemporary look. They're all over Houzz. It works better with a larger vanity than 48" though. You also don't place the mirror right on the backsplash but float it a few inches above. You'd want to change to sconces if you hung it vertically.