Here's the current outlet. I need to leave a cable connected constantly. Is there a snap-on cover for this type of thing? (Can I gaff tape a quart baggie over it?)
I think mark f has already answered your question well. I just wanted to add some photos from a similar project I did last year in case these are helpful to you.
I installed a weatherproof cover and box to replace the old ones that supplied my above-ground pool. Fair warning: don't do this at your own pool because my installation was deficient in several ways; but I bought the house with some problems already existing, and I just needed to make a repair and add GFCI for my own comfort; my city didn't care.
I hope this helps!
I would suggest an update to a extra duty double gang cover. Extra duty or “in use” covers are made to be used while something is plugged in. Taymac mx6200 is a cover that has 55 configurations made by Hubbell this will replace your existing cover and it has switch plates and receptacle plates that snap in so your configuration is what you need.
This is a cast aluminum they cost a couple of extra dollars compared to a plastic one but the difference between plastic and aluminum is, these are tough and last!
I rarely see plastic ones that the cover is not broken or being held in place with tape. This is what I use and recommend I have no interest of connection to them.
The new cover seals against the existing outdoor rated handy box via a weather seal.
You will likely need to put a new cover plate over the switch as well. And be sure the Outlet or entire Circuit is GFCI protected since its outside.