A shed snakeskin appeared when I opened the garage door:

The skin sits atop the retaining wall next to the door, on a stone(-like) background with poor contrast: even an empty snake has good camouflage!
The exterior looks like genuine snakeskin:

I didn’t know the interior has an entirely different pattern:

As far as I can tell, the snake was going about its business elsewhere in the yard.
To be fair, there’s some luck involved.
Update: After Mitch nudged me, I found the (somewhat the worse for wear) snakeskin again. The head end was split, much as I described, but the tail end was intact (the snake having pulled out like a finger from a glove) and what I though was the inside of the top was the outside of the bottom, just pushed inward to form a very thin double layer.
Today I Learned … to always look closer!