My '64 had the same problem. I unhooked the cable from the back of the head and pulled out the inner cable. I lubed it with a synthetic paste type lube as I pushed it back into the sleeve. Use a synthetic paste so it doesn't pump the lube up to the speedo head and so it won't thicken up in cold weather.It has been quiet for years now,
Scott

Scott Ward

2 1948 1.5-ton Loadmasters
The red one and The snow pusher
1 1950 3100
1 1955.1 Chevy 6500
1 1954 Chevy 6500 2-Ton
1 1955 1st Series COE 5700
1 1963 K20 (454)
1 1964 C10 (350)
1 1951 1.5-ton Dump Truck
1953 and a 1956 Ford F800

Raising a teenager is like trying to nail Jello to a tree!