Likely you've got a whipped upper or lower cable, or, it has begun to come uncoupled at one of the four connections it has. (trans to lower cable, lower cable to that stupid tripometer box in the inner left fender, inner left fender box to upper cable, or cable to speedo head)
If it's a loose connection thing (I personally doubt it) then snugging those up should cure it, other wise you'll have to determine if it's the upper or lower cable and replace whichever section, or, take the easy way out that actually works very well and get the one piece cable setup from an S2 then bypass that tripometer thing all together. (all it does is turn on that 'exh sensor' light on the center console once every 30k miles to remind you to replace the O2 sensor)
I have a similar problem with my 82 Question? Does the odometer still work? The interesting thing with mine is the odometer work perfectly even when the speedo stops working. Mine only works for the first couple minutes but used to behave like yours. I have taken the cables apart lubed them and checked the ends and tightened everything. Eliminated some bouncing of the needle but did not solve the problem. I plan on taking my speedo apart. The speedo is driven by a magnetic coupling inside the unit and the odometer is driven by a gear inside - both driven by the same input cable. So since the odometer works the problem should be with the magnetic coupler and its bearing point of the magnet wheel and the pointer spindle. The article by Anthony Rhodes "repairing Jaeger & Smiths Speedometers" is going to be my guide.
This is interesting seems my speedo does similar things, only that it will run correctly for about 30 to 45 minutes, then zero's out. I slow down to about 10 mph and take off again, it works for a while again. Any Idea's?