Bouncy needle on speedometer

I always pull the inner cable out, than I feed it back in while working grease all over the cable that way it stays for awhile.

Yes, just pull the inner strand out of the conduit (outer sleeve) and lube it. Then replace the strand in the conduit the same way it came out and then put it back on the car.

Maybe use a lithium type grease or light oil like 3 in 1 oil or similar....

Also note that the ends of the strand are ground to a square shape, try to line that up with the fittings at the trans end and speedo end to make sure that they mesh together properly when putting them together. The mating ends in the trans and speedo are also square and sometimes don't go together properly, you have to pay attention when assembling and feel for it and sometimes try to line them up before putting them together.