2002 Lincoln Continental

You don't have a "V-12", you have a "4.6L DOHC V-8"

And are you saying that all of the needles move like this, or just one (Speedo)?

If all of the needles move this way, then your problem is either a bad connector/wire to the cluster, or the Body Control Module is failing.

If only the speedo does this, then either your vehicle speed sensor is bad, or your crankshaft position sensor is bad. (If the engine runs/starts fine, then you can rule out a bad Crankshaft position sensor)