antenna issue: only AM works

[gloves12]

Hi! I'm trying to troubleshoot my stock 99 Lumina radio: in recent years, only the AM works, no FM. In extreme cold (sub 0 fahrenheit) the FM starts working again. Sometimes it comes in and out, like this:

In the past, punching the radio face consistently fixed the problem (coolest road-trip trick ever), but not any more.
I'm guessing it's the male antenna connector that plugs into the back of the stereo? I've replaced the stereo (identical factory unit), exact same problem.

How does the AM / FM work, do they both use the same antenna? Thanks!

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