Your cousin is probably right in guessing that it is lifter tick. I have heard of some people using that mystery oil stuff and it clears it up.
Jumping? Like, studdering? If it does away when you let off the gas, it probably isn't suspension/wheel related. It is probably misfiring and needs plugs and wires.
What is the history of this car? Mileage? Maintenance?
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Corey Smith