The easiest thing would be drill a wall anchor above the outlet and secure with a zip tie but that might not look very neat.
If you use that method,... I would recommend you use what is could a Plastic Toggler for the wall anchor. It’s clean looking and it really holds when installed correctly.
Drill a 5/16" hole in the drywall for installing Toggler. I assume it is 1/2" drywall...
From the manufacture:
Grips and locks on walls or ceilings 3/8-in to 1/2-in thick (e.g., residential drywall) for medium duty holding, but also works if you hit an unexpected solid, like a wood stud. Holds up to 143 Lbs. in 1/2-in drywall with #8 x 1-1/2-in Combo head screw included in the package. (Industry standards recommend 1/4 of this ultimate load per anchor. see our technical bulletin.) also works with any screw #6 through #14 with a minimum thread length of 1-1/4-in plus the thickness of the item to be anchored. Needs only a 5/16-in drill bit
FYI IF the outlet rough-in box is a standard 2" wide, nominal, (which more than likely it is), The box will be fastened to, (I assume), a wood stud. If you are going to center the anchor exactly centered on the outlet, above the outlet, use care drilling the 5/16" hole through the drywall. Stop the bit just as it goes thru the drywall. You don’t want hit any Romex cable that may be stapled to the Stud. It’s suppose to be stapled in the middle of the stud, BUT! Don’t take a chance. Also I would stay at least 6" to 8" above the top of the box to avoid the chance of hitting any Romex entering or exiting the top of the box.
When installing the Toggler install the wings vertically.
You might want to fasten something like this to the anchor on the wall.
Mounting base . With this base, if it will work, use a flat head sheet metal screw to fasten it to the anchor. The FH of the SMS won’t interfere with installing the Tyrap through slots in the base.
I would probably use at least a 3/16" wide, maybe a 1/4" wide Tyrap. Use a black color Tyrap. Not a clear...
Hmm, Have you thought of using a Velcro strap instead of a Tyrap, zip tie?
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FYI, I have an idea for a plug support, using a flat metal bracket that will fasten to the bottom 6/32 machine screw that supports the bottom Yoke of the wall duplex receptacle to the wall box. The trap will have a slot that will allow it to slide between the outlet support Yoke and the box. (only the 6/32 screw will need to be loosened to install the bracket.
The flat bracket will go down just below the bottom of the outlet wall plate then turn out away from the wall around 2" and then turn up toward the plug body of the plug. I’m still working on how it will turn horizontally under the bottom of the plug. Also I thinking about making the vertical riser and the piece that supports the plug two pieces . Splitting the two will allow the riser to be adjustable for different outside diameters of plug bodies being used. It’s a work in progress.
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