Hi bentwood,
Welcome to the VCCA's Chatter forum website! This is the best place to ask such questions and hear the thoughts of kindred, old Chevy enthusiasts!
The speedo cable unscrews from the side of the transmission so you can inspect it. You do not have to remove the tranny or anything else.
If I remember correctly, the last time I had this connection apart on one of my trucks, I cleaned up the nut and cable housing end and then smeared some Permatex Aviation Form-a-Gasket on the threads on the tranny and a little around the cable housing where the nut seats.
Cheers, Dean