Here's a quick way to lube the speedometer cable from the transmission side. I didn't feel like tearing apart my dash just service the cable.
Basically adapting the small red tube from a can of white lithium grease to a piece of rubber with a hole in it like a piece of tube or anything that can seal against the speedometer cable outer housing. Pushes the lube up the housing. I had a cone shaped air hose tip laying around. Used a vacuum nipple cover and poked a hole in it for the small red tube. I'm sure you can piece together something better at a hardware store but this is what I had laying around.
My cable no longer bounces or makes a noise.

Basically adapting the small red tube from a can of white lithium grease to a piece of rubber with a hole in it like a piece of tube or anything that can seal against the speedometer cable outer housing. Pushes the lube up the housing. I had a cone shaped air hose tip laying around. Used a vacuum nipple cover and poked a hole in it for the small red tube. I'm sure you can piece together something better at a hardware store but this is what I had laying around.
My cable no longer bounces or makes a noise.