What happens if you try to drill right through the plastic-like face of it? Does the drill bit carve right through, or does it shatter the reflector all over the place?

I was considering putting a reflector on the back of a fender, but it'd take some rigging, so I'm trying to figure out the best way to go about it.

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I haven't done it, but I bet if you drilled a pilot hole with a very small drill bit, and then enlarged it with a larger bit, you could do it without shattering it.

Here ya go

https://home.howstuffworks.com/type-of-drill-bit-plastic.htm

Yeah you can drill it, but unless you have a specific reason to use a particular reflector it would almost certainly be easier to buy a suitable one for your purpose off-the-shelf.

Also, reflective tape works very well for this purpose.

Others have answered the question about drilling, but as a side note I prefer retroreflective tape for my commuter bike--you can get it in all sorts of different colors that blend in well with the bike frame, fenders, etc, but are insanely reflective when lights hit them at night.

^^^^ This.

Except for most LBSs have a huge box of reflectors, taken off bikes whose new owners wouldn't be seen dead with a reflector on their bike. Mine let me have a couple for free. Get the ones that are typically used to mount on those plastic seatpost clamps. They already have a screw hole for mounting. Might as well get the screw too while you're there.

Then you just need to drill the fender. On my SKS P-series, the bracket for the lower rear fenderstay already had a hole, so it was simply a matter of extending it through the fender. A little Locktite on the screw and it's been there forever. All it cost me was a little time and a drop of Locktite.

If you do, I suggest something called a spade drill. When drilling thin sheet materials a twist drill (What most call a conventional drill bit) will try to grab and pull the material.

You can get these for a lot less at home depot, but I couldn't find an image easily on their site.
Spade Drill Bits products - Grainger Industrial Supply

Here's the Home Depot site: Ryobi 4 Piece Steel Glass and Tile Bit Set-AR1650 at The Home Depot

You can drill through glass if you have the right tools. I've done it.

you could poke a hot steel rod thru the plastic rather than worrying about shattering the plastic, drilling..

if wanting to mount it with a screw through the reflector

think about how you wont crush the reflector tightening the screw.

IDK of many glass , non antique , reflectors ..

Might try drilling from the back. Wear eye protection in case it shatters. Good luck!

I second the use of a glass/tile bit.
Put masking tape just in case. I was
able to drill glass without it shattering:

https://www.youtube.com/watch?v=1v9Z...6zPoymgKaIoDLA

Drill the fender, only.

Reflector ? Rear Fender Mount (SKU:2203) | ISO Bikes

They are also available on ebay. Search "bicycle fender reflector"