Long story short, I got a free mirror, but I had no way to hang it (besides taking a trip to the hardware store, but come on...) so I modelled something quickly in Fusion 360 that works great!
You can download the file at: https://a360.co/2Df6cyT
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Step 1: Basic Design
I used Fusion360 for the design of this bracket. After taking measurements for the thickness of the mirror (mine was 4mm), I started off with a simple L shape, with a top cap to actually hold the mirror against the wall.
Step 2: Tweaking
After that, I realised I needed to crate a bit more space for the screw holes, so I used the push/pull command to extend the outer walls by about 5mm in each direction. I then added the 5mm screw holes.
Step 3: Polishing
With the screw holes added, I filleted the edges of the retaining section of the bracket, and added a chamfer to each of the holes. I then outputted it to slic3r.
Step 4: Slice and Print
In slic3r I set an infill density of 90%. I'm not sure that this was entirely necessary, but it gave me some peace of mind at the very least. I then printed four brackets at a speed of 50mm/s on my Ender 2.
Step 5: Installation
I inserted Rawlplugs into the plaster board and then screwed in the bottom two brackets. After dropping the mirror into place, I screwed in the topmost brackets and could fully enjoy the use of my new mirror!