I am looking for the percentage of people who relocate from a rented
housing unit to an owner-occupied housing unit and the number of
people who relocate from an owner-occupied housing unit to a rented
housing unit, and a reliable third party source I can reference for
these numbers.

It can be as simple as 20% of people changing their primary residence
change from a rental unit to an owner-occupied dwelling and 15% change
from living in an owner-occupied housing unit to a rental unit.

$100 tip for anyone who can give me this data broken down by MSA in
one form or another.