I think it is important to taper it and make it a wedge and not a spacer. They do have a functional purpose, which is long winded. The amount of taper on the wedge is the same as the taper on the tang.
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You mean the resultant separation at the pivot between the scales should be the same size as the tang? One thing that comes to mind is that this presumably creates added tension and friction in the closed position where the shank pinches between the scales. Not sure if that's right considering the washers at the pivot, just filling in the blanks.
I'm working with really stiff scales, so there won't be any flex.
Scales really need to flex otherwise they will not function properly. What Rezdog was referring to is the need for the scales to have a slight bow in them when fully assembled - this is achieved by creating a wedge. If you pin the wedge in position, leaving the scales loose at the pivot end you will see that they create a V shape. Now when you fit the pivot pin, the scales have to bow because of the wedge shape. If the wedge taper is correct i.e. about the same as the taper from spine to pivot, the blade will fit without binding on the sides of the tang.
Without a bow in the scales - for example if you fit a spacer instead of a wedge, the sides will be pretty much straight and the razor will have to be forced into the scales.
So, back to your scale material - you need to either thin it out to allow some flex, or maybe reconsider what you intend using if there is no possibility of it flexing.
Not that it is the same size, but the same amount of taper. The tang has a certain taper to it, some are more dramatic than others. In order for the wedge to do it's job it needs to have the same amount of taper, it is typically quite a bit thinner than the tang.