You don't say how long it's been since you either lubed or replaced the speedometer cable.
The flailing is what happens when it dries out, or when it's worn out and needs to be replaced. Mine started that at about 2500 miles. I lubed it then, then 1000 miles later at the 2nd oil change, and again once and it didn't really help much so I replaced the cable. Haven't had much trouble since then, possibly because I lubed the new cable really well before I installed it. (I soaked it really well with Liquid Wrench chain and cable lube.) It has recently started being a little wobbly after 30 miles or so on the highway, so I just lubed the second cable tonight for the first time since I installed it. (Not sure how many miles that's been, but I think about 5000, so a lot better this time.)