Recommendation? Looking for someone to drill and tap some screw holes for a pocket clip.

It depends on what the material is. Bottoming taps are normally only used for finishing the last few threads in a hole that's already been tapped as deep as possible with a plug tap. On very soft material like plastic, brass or aluminum you might get away with it, but tougher material will give trouble.

There are three varieties of tap - taper, plug and bottoming. The only difference is the amount of tapered relief ground at the end of the tap. Bottoming taps usually have almost none so that they can thread nearly to the bottom of a blind hole. A plug tap will have tapered relief for around 4 threads and a taper tap might have double that.

What that accomplishes is basically allowing a sort of gradual cut, with the first taper ground tooth removing very little material and each following tooth taking a little more material. At the end of the taper, the first full tooth finishes the thread, and the rest of the full teeth should do nothing but follow the existing thread.

All of that said, in the machine shop we mostly used plug taps for everything. If we needed a blind hole threaded all the way to the bottom (not very often, usually we were able to drill the hole a little deep and just use the plug tap to full thread depth) we'd put a bottoming tap in by hand and finish the threads at the bottom of the hole.
How deep did you take the hole?
 
How deep did you take the hole?

Just deep enough...:D

You'll need to see how long your screws are first, then subtract the thickness of the clip where the screws go through. Next take a peek at your tap - add whatever the length from the end of the tap to the end of the taper grind is to your initial depth number. You want to make sure you go deep enough with the drill so that the tap is able to produce the right amount of full thread or the screw may break or strip out the threads when you go to install it. Also don't want to go too deep or the drill may break out the bottom of the scale depending on where the hole falls.
 
BTW, in this application I would shoot for at least 6-7 threads full engagement but no more than 10. If the screws are too long, cut them off to get the right amount of thread engagement. If they're too short, get different screws.
 
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