For small , thin pieces (like wedge plates, etc) you can use Sealing Wax.
(Envelope Seal and Document Seal wax impression)
A Jewelery Engravers 'trick' of sorts to hold similar small fragile items while engraving.
The wax comes in sticks with a wick in it usually like a candle. Light the wick and let some of the wax drip into a pool onto a suitible surface like a piece of wood that you can work on.
The wax if still warm enough, you can push the wedge plate or what ever part into it and as it cools it will adhere nicely for you.
If cooled,,heat the part and push it into the cooled off wax.
Do your engraving.
When done heat the part back up gently and it will drop off of the wax.
I used to hold the part up close to a pre-Al Gore filiment light bulb. The heat more than enough to make the part loosen and drop free.
Same idea as the Pitch Bowl. Less holding power though so for smaller items. The sealing wax sticks are cheap at art supply type stores.
The puddle of wax left on the piece of wood is reuseable over and over, or add to it, etc.
I engrave some of the parts while inletted in the wood. That's a real pain as I have to stand and engrave. Not a favorite of mine.
Moving around a LR from end to end is no fun.
I rather like to just attach patch boxes, butt plates and the like to a piece of wood simply roughed out to form and the part screwed down in place.