If you have surely identified samples of the candidate materials AND you can take a sample from the part, one excellent method is to burn them and compare the smell. Even the human nose distinguishes many polymers like that. The aspect of the flame tells also much.
Isoprene should smell like polyolefins (polyethylene, polypropylene...) which remind of candles, but the chloride-containing isoprene will be very different, supposedly similar to polyvinyl chloride.
Please burn small amounts and not in your closed kitchen. Burning Pvc is nasty for real. Near you nose slowly, no more than needed.
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The second method is the density. Neoprene is clearly denser than water (>1230kg/m3) and sinks. Butyl rubber is mainly a polyolefin, with density around 920kg/m3 so it floats on water. Eliminate all air bubbles for the test.
That would be for pure formulations... Rubbers are often blended.