They make specific lighting boxes for this application, they are usually round and while not necessarily waterpoof, they're typically painted or made of plastic that's not going to corrode in such an environment. You'll have to check the instructions for the fixture, but most decorative ones won't work on just a pancake box.

It sounds like with our exterior foam insulation, you might have sufficient depth there for this box (just screwed to the disoriented strand board).

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.