The job is done. It turned out that there was no box, and therefore a good thing that I bought one just in case. They, of course, had one ready to be installed. But it was grey, and the one I had bought was the same color (white) as the siding. It also turned out that the wiring was Romex, not knob & tube, so that worry of mine was unnecessary. Thanks again for the information and the offers of assistance.
Ethan, I would also love to meet another forum member. I think I have only met four to date. Perhaps we can get together at some point while you are in town. I work at home, and home is in the Broadview area, about 10 miles north of downtown Seattle.
I will post "before" and "after" photos later. But I don't think it right to share the cost of another electrician's work.