It could be the center support bearing. I had a shake at about 45, their was just a slight amount of side to side play if you grabbed it and tried to move it.

The center bearing support is rubber and was worn, I also replaced the bearing itself. Now no play really, just a little movement because it is rubber mounted.

The drive shaft is in two parts, their is a spline that mates the two halfs together. I don't see how that could wear. Well at least mine at 250k looked like new and was tight as can be.

I'd recomend removal and inspection, maybe bring it to a driveshaft shop for a balance and see what they come up with.

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2016 Corvette Stingray 2LT
1969 280SE
2023 Ram 1500
2007 Tiara 3200