Leo- I use a lot of wood from Ocooch hardwoods- they have *very* nice scrollsaw wood and also .25 mdf core ply that cuts very nicely- more uniform than ply.
You might try certainlywood.com. They are a veneer supplier and have 1/8” veneer in some species. They sell large or small quantities. The pieces might need flattening. The website will show the specific flitches in stock with the pricing.
A search for "Thin Lumber 1/8" like this : https://www.ebay.com/sch/i.html?_from=R ... =thin+wood
comes up with a lot of option, some quite reasonably priced. I bought some a few years ago, but the problem is that such thin lumber will warp or bow significantly and just not stay flat. I used it for vcarve inlays and glued flat to a carrier board that was not such an issue. But stand-alone it can be annoying.