I'm a pro with a big shop full of cool machines. But when I need to enlarge the ear notches in a pickguard, I would do it with a file. It would be faster and neater than a router or a drill press, or even a hand punch. Really. Pickguard vinyl is very soft and cuts easily.
One trick to make it easier is to find or make a hole in your workbench. Hold the pickguard flat on the table and the file vertical, going down through the hole. That way you can easily see what you are doing, and the pickguard is supported well by the table.
Here's my cool special custom pickguard filing sub-table, which clamps in the vise on my main woodworking bench. I made it just for doing trim filing of pickguards. You don't need something this fancy, but you get the idea.
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Doing the filing with a 8" Round file. Here, I'm actually filing out some P-pickup openings. This was a one-off, and it wasn't worth the time to make up a template and cut it with a hand router or a pin router.
I traced the outlines of the covers on some masking tape, drilled a bunch of holes, and filed the openings to shape. Including the ears. No big deal, and only took maybe ten minutes.
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I finished up the shape with square and flat files, then cleaned up the file marks on the edges with a small scraper.
Files are a Luthier's main tool.