The cable may need a lubing with graphite or something, if it seizes and snaps you might get this. Should be a quick fix.
Your speed sensor may be going out or the cable may not be firmly attached.
Possibly your speed sensor. My speedometer would bounce around & then soon after it felt like my transmission was slipping. Turns out the speed sensor controls the upshift in your transmission.
I would suspect a faulty VSS. Try replacing the vehicle speed sensor in the transmission.
sounds like a broken speedometer cable.
== ==
About the only thing that will cause the wheel to bounce on any car is the strut being bad.
The gears in the speedometer are stripped. If the odometer is working then you have input.
TCM Malfunction, And/Or Speedometer Sensor Malfunction.
If it's an electronic (analog) speedometer needle, you probably have a problem with the dasboard grounding.
i would have to bet on the speed sensor
The speedometer on a 1996 Honda Accord EX is the pulse variety. It is likely that the teeth on the speedometer gear are not meshing properly.
Faulty vehicle speed sensor.
If the speedometer continues to work - probably a broken gear etc. in speedometer head and probably will have to be replaced. If speedometer does not work -- probably a broken speedometer cable