Well--you got a variety of answers there!
isn't hard to work with, but making the repair semi-invisible might be a real challenge. I wonder if a workable solution might be to create, in effect a radio-block-off-plate, and either glue or fiberglass
that into the opening.
If it was me, and I was doing it to my U-Haul
[similar to your Burro
], I'd  start by getting a piece of rigid, smooth-faced plastic a little larger than your current tape deck hole....... make it "tidy"--straight-sided, with slightly rounded corners..... trace around it on your Burro's closet skin, and then slightly enlarge the existing hole to match your new plate, until the plate just fits the opening, and then tape it in place on the "good side" of things........ glue a patch on the inside of the closet that bridges over the gap between new and old.
If you want to do this with fiberglass, you can get a small kit [probably
] in an auto repair store that deals in auto-body fillers and paint
And then on the side that shows, you can mask off the surrounding area and spray-paint the new patch something close to the original color. It won't be exactly the same, and you'll see a thin seam-line, but it should look neat & tidy. And you'll have done a little f/g repair!
p.s. There's a really long thread on this site about f/g repair that I studied a lot before diving into my own project..... I think the author went by "Fiberglass Dave". Lot of good tips in there.