Any needle bouncing is actually the drive cable is stopping and restarting every revolution. It means there's maybe individual wires in the cable that have broken or the whole housing is dry.
I don't like taking the cable end of the back of the speedo - but it IS do-able if you're dedicated...
Boomer-type guy here with a 1986 K5 Square, 383 stroker, Crane cam, Edelbrock Lo-Riser, THM700R4 with some goodies, Gov-Lok rear, Posi-front, Warn Hubs, Warn 9K winch, 265/75R15s on 2000 C-K 4WD rims ...................... it's orange.