On the other hand, it made it way easier to get that wire down into the downstairs area. (We've been calling it the basement although it's above ground. Sort of a well-lit basement. It feels like a basement. It's not a garage, because it has no garage door. Must be an above-ground basement.)
I answered my question with this: "How do you attach things to a brick wall?" Answer: nail it or screw it. I used drywall screws; they just zoop right in and hold fast. (Well, I twisted the head off one.) It was pretty impressive, and that heater is well-attached.