Some of those mounting plates are only a few inches wide by a few inches tall. The 1/4" plywood is a a good size but if it were me, I'd make it wide enough to secure to a couple of internal studs on each side in the wall which you should be able to locate using a stud finder and/or the good old knock/press method where you feel for the firm vs. spongy section of wall board.
If you can identify a wall stud on each side and get a screw through the top and bottom of the plywood into each one, you will be solid and never have to worry about it coming loose. There is a lot of torque on those wall mounts, especially if you use an articulating arm that is not fully compressed against the wall and locked, bungeed flat.
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2020 Chevrolet 2500 LTZ, 2019 Forest River Wolfpack 23Pack15, 2014 EZGO Golf Cart.
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