Speedometer reads 20 to 60mph while sitting still

Just a stab in the dark because I am not certain how a 98 Western Star is wired but what may be happening is when the truck is in motion the speedometer is reading off the wheel speed sensors but when stopped it may be looking at the transmission or tach signal to determine if the engine is running, if one of those sensors is failing or has a loose connection it might be able to cause your symptom.

I do know that on peterbilts of that era the plug in for the speedo and tach behind the dash gets loose with age and causes erratic readings, I have had to use a small zip tie to pull the connectors sideways to keep them connecting well on several older trucks but the symptoms never went away when in motion on those.

 

Any recent repairs? New speedo gauge?
Usually this is caused by electrical interference if it works perfect down the road but is reading erratic when parked. For awhile the new amtek 900 series speedos were made too sensitive and did exactly this. They then fixed up the speedos and the new new ones do not have these issues.
Check for a loose yoke and follow the wiring up to the engine looking for any rub spots or corrosion.