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For your application it would be "headliner windlace". It's a vinyl/plastic material molded over an internal metal core w/the metal core providing bite/retention and some stiffness to the headliner windlace pieces.
I don't know that anyone repros these with the original TEXTURED/GRAINED appearance. You'd have to check around.
You might consider removing yours, wiping them A LOT w/clean towels and something like lacquer thinner to remove the "gooey-ness". That will take awhile...repeated wiping/scrubbing w/the solvent soaked towels.
Then you could try spraying them w/a adhesion promoter and a vinyl/plastic paint like SEM Landau Black. The vinyl paint has flex agents in it but you'd want to avoid bending the pieces sharply/aggressively once painted.
EDIT: Checked on the internet and it does look like some repro places make these with the original appearing grain. BUT....you want to make sure any repro also has a metal core or some integral metal clips for retention.
TPP's description says their windlace has integral steel clips for retention. So....maybe not a full length steel core like the originals but MAYBE sufficient. To me, you want retention along the full length so no risk of sagging, etc. No full length internal steel core might allow sagging....who knows?
I'm using a repop front windlace. They're OK and hold onto the headliner just fine but it is certainly best to rescue your original if possible. There might be someone here that has a very good one as well. The repops are only black so you have to paint it. Only the front is repoped - none of the others.