I threw an old set of TV rabbit ears in the trash.
Then I took it out of the trash.
I peeled off the felt on the bottom and removed the steel plate.
A screw holds each antenna on.
I drilled out the rivet head.
Then punched out the rivet.
Leaving me with one telescoping antenna.
I counterbored a piece of steel to accept a magnet.
And drilled the other end to be a slip fit over the antenna end.
Epoxied together. Now I have a slightly cumbersome telescoping magnetic pickup just like one that you could buy at the dollar store.