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i've used a combination of graphite powder and a light machine oil, like 3 in 1 oil. white lithium grease or any grease for that matter maybe a little thick, especially in colder climates.
GM used to have speedometer cable lube which I've used with success many years ago when I was stripping speedo gears. Don't know if they still have it but worth asking. As I recall, it was a thin black grease, probably molybdenum disulphide.
Any auto parts store will have the cable lubricant. You can apply it to the 2-piece speedo cables easily by disconnecting the connection between the upper and lower cables. Squirt the stuff in there while holding the ends higher then the rest of the cable and give it a chance to soak in good.
All the major suppliers also sale a grease fitting that screws on the end of the cables for lub. They also sale a 90 degree fitting with a grease zirk for your tack that will take the sharp bend out of the original cable for longer life and is easy to grease without disassembling anything for those of us who did't know. It runs about $35.
Haven't had issues with a Corvette speedometer or tachometer cable yet. A couple years ago I had a noisy speedo cable on an 86 Chevy PU. The movement of the speedo indicator needle would tend to coincide with the noise.
Removed the cable and the housing from the truck.
Pulled the cable out of the housing and examined it. It looked OK so I decided to reuse it.
Held the empty housing over the trash container and soaked the inside with brake cleaner and WD 40 until it was clean inside.
Did the same thing with the cable.
Was leary of using white grease so I used motorcyle chain lube.
Soaked the inside of the housing and the cable with the chain lube and reassembled.
Worked like new, no noise, no needle flutter and no problems so far.
67-73-76 touched on using motorcycle lube for the chain, but they actually have a lube for M/C cables for older bikes. All the cables on older bikes were mechanical cables-speedo, tach, brakes and clutch; the lube for these held up pretty well since it was designed for exposure to the elements. Maybe harder to find now due to technology advancement taking place of these cables, but the lube worked excellent-can't recall the name but an internet search should pop something up.