I've cleaned and lubed the speedometer drive cable on my '81 about 7 times in the last 29 years .
I take a plastic bag, cut the corner out of it put it over the cable conduit put a ty-wrap around it to get a somewhat leak proof seal, put some alcohol in the bag .
With the cable at the transmission end chucked into a drill motor, turn the drill motor on the alcohol will flow down and clean the interior of the conduit .
Do it a couple of times until it looks good to you .
I use a light air tool oil, do the same as the alcohol, but it gets a bit messy at the drill motor end when you use oil .
Don't use anything like WD40, it turns into a sticky varnish over time .