Hobby stores carry "K&S Precision Metals" as well as some Home Depots or Lowes, IIRC, in very thin sizes.
As for 'clamping' these thin or thicker metals down, apply a touch of 3 Pound Shellac to a piece of card stock, something no too flexible, and put your pinhole material down so it is glued to the card when dried, throughout.
Drill your pinhole, and when you are finished, simply place the card stock with brass pinhole into a jar with some alcohol, until the brass work slides off the card.
You can do the same with thread fastener, such as Loctite 222, Purple, but use acetone/nail polish remover to free the piece, as above.
This way, you do no chance bending your pinholes as you try to remove them from double stick tape and you do no have the brass stock flexing up and down when mechanically clamped to a work surface.
You could try sandwiching the thin stock between two solid layers of wood, metal, etc, but the shellac should serve you well, and Bullseye Shellac is found in many home shops and stores, just do no thin it for best results, IMO.
Before writing off Harbor Freight tools, look at the item you are considering and read the reviews to get an idea if it's a "gem' or a lemon, the online site allows reviews to stay up no mater how negative one might be.
Also, there are list of best buys from HF, as well as list of 'no with a ten foot pole' be aware tools.
There are many, many people who use the buy and re-buy approach to HF power tools for their own use or for/by their company.
I'll also point out that manual tools, such as screwdrivers, wrenches, hammers, etc, now carry the same "if it breaks, we'll replace it" warranty as old Sears Tools, so you can simply bring in a tool that has been broken, (no by deliberate abuse) and walk back out with a replacement.
Personally, I like the small burs,endmills and diamond bits and drills sold by HF, and will likely try using them on upcoming pinhole projects, but that is a informed, personal choice.
IMO.
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