Working in a ford dealership many years part"s department had a specific lube made for speedometer cable, it was a very light grease almost clear looking. I lubed many cable"s that were noisy and had some quiver to speedometer needle.I had a few of my own vehicle"s that I used this and fixed the noise and quiver, in fact the 66 chevy I now drive. Probably unable to find any more grease like that ,but I have seen white lithium grease as a alternative and or graphite powder.No need to remove housing from vehicle, just disconnect cable from back of speedo and pull out center flex cable with a needle nose plier"s and wipe clean and as you feed back in housing apply a coat of what ever you use all along the cable. When you get cable in close to tranny just keep tuning it and it will go back into the gear.Just make note how far the cable is in depth in the housing before you pull it out and you will know how far to go so you know it"s in all the way.II would try this and if it is still there then speedo need"s repair.PS I just found on another site post other than here that O"Reilly"s sell speedometer cable lube in a small tube.