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Suddenly, the car is jamming AM radio stations.

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I think the torroid chokes are on some cars, and not on others. Not sure what models, serial number, or country-specific versions have them. For what it's worth, mine doesn't have them either.

I'm not under the impression that these are things that simply clip on to the cables, rather the cables have them molded on. If so, they're not something that was left or fell off.
 
Pretty sure they are only on EU cars. Not US. You can certainly add them, as they are just donuts that the wire passes thru.
I second this. I've only seen them on EU Roadsters, never on a North American Roadster. I've never tried to use my AM radio. You're the only person I know who has. Chokes are cheap to buy. You don't have much to lose by trying some.