I keep reading recommendations to fasten templates to stock with "carpet
tape" for template routing and to use "carpet tape" for various other
operations. In some videos a tape is shown that is wide, thick enough
to be a little bit conformable, and apparently a solid piece of plastic
film that peels off in one piece, but they never give specifics or show
the container.

The "carpet tape" I find at Home Depot is miserable stuff, basically a
bunch of fiberglass strands in adhesive, that peels off in shreds and
ends up having to be scraped off.

So, can someone recommend a brand and product name or SKU for the stuff
that actually works for this purpose?