Thanks for the replies y'all.

Granny, I have been using a bona-fide weatherproof cover (i.e., before
I've plugged in the shutoff switch).

It's actually much deeper than the one you specified, crash. A
right-angled x-cord would still be too much to fit in it.

Bill, covering everything with plastic and putting under a pot should
work, except when the city inspector comes over and frowns at it.

There must be a correct way to do this; I'll call Little Giant, the
makers of the switch, tomorrow, and see what they say. I'm not the
first to come up against this....