1999 Mercury Sable 4 Door Sedan

Intermittent cruise control and speedometer problem

Need advice on how to fix this problem

Is the Check Engine light on?

Tester

Make sure all the speed sensors on the transaxle are working correctly

No the check engine light is not on.

More than likely a speed sensor problem; CEL or no CEL.

Back in those mechanical days, the speed sensor is driven by a plastic gear…prone to wear. That needs checked as well. Remove the speed sensor from the transaxle and look. The gear has angled teeth but the surface of those teeth should be level, not concaved.
Look down in the hose where the speed sensor goes…the gear down inside should also not be concaved.
A worn out gear may be spinning sometimes but lose contact with the drive gear explaining an intermittent proble for both the speedo and cruise.