Bought a 19-4 on gun broker. Gun locks up tight when in battery. What I did notice is that when the cylinder is open I can move the cylinder back and forth on the ejector rod about 1/16" inch. Is this normal? What is this movement called? How can it be corrected? Thanks.

That is totally normal. Actually the cylinder is not even attached to the yoke, it free floats and is only held on by that little bump by the thumb piece when it is open. You're good