From the speedo itself down to the wheel; the entire cable and sheath. Sounds like yours may be dry, and the cable is rubbing against the sheath, causing the "jump' you are seeing. I use wheel bearing grease, but you could also use silicone spray, like the guy in the video, or chain lube. If you use grease, run the cable through the sheath, rotating it as you go, to coat the inside of the sheath with grease. Then remove the cable and wipe off any excess grease and install.
I used a little engine oil to "clean it out" and then finished it with few sprays of white lithium lube. the difference is night and day. There is still a tiny bit of needle jump but it is only noticeable if you are looking for it.