1999 Lincoln Continental stheering wheel shakes

Can you be more specific? A lot of different symptoms can be referred to as "jumping". Does the car have to be moving? Do you see the steering wheel move left and right while you're driving slowly through a parking lot? How does it steer on the highway?

This is best handled with an inspection at a tire and alignment shop. A broken belt in a tire can cause this but you'd feel that when going straight too. Same with a bent wheel. I suspect there's an issue with the power steering pump, (weak output), a loose drive belt, or something like that. There can be internal leakage inside the steering gear too, but to affect steering in both directions is not common.

Check for a spring-loaded tensioner pulley. Sometimes they rust in the pivot bolt and don't provide enough tension on the belt.