Thank you, ronnatalie. I looked at and measured the round boxes. They were 1 1/2" to 2" deep, too deep for the 1" rigid foam. Oh foo. I finally got an adjustable depth single gang PVC box. I put a 2x4 cleat across the space and an 18" long stud vertically to hang the box. The metal bracket fastens to the face of the 2x4 so I first fastened the box to the wood then rotated it to the outside and fastened the stud vertically. The adjusting screw made it simple to set the box exactly to the face of the foam. I will add a vinyl mounting block and flashing tape to divert rain around the j-box.

Don't know about vinyl siding hanging stuff, but I do know how to hang a really heavy weight mirror. In fact, my DH is in the process of hanging one inside our Cape up in Massachusetts now. It takes two boards, one mounted on the wall and one mounted on the back of the mirror. The long edge of the wall-mounted board is sliced at an angle to allow the mirror-mounted board to mate with it, and thus spread out the load across the width of the board. If I can draw it out for you with keyboard strokes, I'd do it. ]__\ is the basic shape. The slanted angle is on a long edge of the board. I'd make it a 2" thick board at least. The two boards come together so that the edges are like this \\ .....Hope that shows you. With your mirror, a second row of wood near the bottom might secure it against any wind trying to twist it. But basically, this will hold up a LOT of weight.

Screenshot of all

Looks like that is going to be a lovely outdoor space with a view! I really like the siding without the stone. It looks classic. I'm a fan of white houses. Once landscaped, it will be beautiful. We did a wood ceiling like yours, for our front porch. We stained it somewhat dark. It certainly provided added character. Haint blue is another great option, especially if you're in the south! We were not. All personal preference on the look you're going for. Please share your 'after' photo when completed :)