That sounds just like what the cable in my 81 Burb was doing.
Easy fix it, took me about 10 minutes.
There is a clip on the speedo, just pull it out a bit and the cable comes right out.
then pull it through the fire wall and follow it to either the tranny or the cruise control on the fender if you have it.
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69 K5, .060 over 350/465/205.
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