Dunno how to get to the cable, but use graphite, not oil.

If your speedo cluster is anything like the 89 Cavalier Z -24 I had -
and the Cimarron is based off a Cavalier platform. It was pretty easy to
remove the cluster.

My 89 had all kinds of visible philips head screws to remove the trim
and dash panels around the cluster. A few screws around the outer
diameter of the cluster held the cluster into the dash.

Pull it forward remove a few wire plug ins. On the 89 cluster a round
spring band held the speedo cable end into the back of the cluster. Once
the cluster is puled forward I think you can squeeze the spring band to
release it. Once the cluster is out of the way you can pull the cable
out & lube it.

Looking at a shop manual would be a good starting point too.

Good Luck

Harryface

Hi
I just want to tell you guys that I was able to unscrew the speedometer
cable at it's connection on the transmission under the hood. It was hard to
reach but not impossible. With the cable lose I could turn it "upside down"
and "fill" it with a thin oil. And the sound is gone! (At least for now!).
Thanks for all the tips.

Roger