Cleaning it out of the car is as easy as standing it upright and putting Evaporust inside the tubes one side at a time. You'd have to do a general degrease cleaning first and plug the ends. Blocks of wood bolted on with wheelbearing grease as a sealer on the brake backing plate flanges to keep the rust removal fluid from leaking out maybe?

In the car is harder. Possibly a large engine bore size cleaning brush and run it inside the tubes I guess would be good for knocking the majority of the loose stuff off. Wash it out with degreaser or solvent and blow it dry. The overlap seam part in the middle of the housing behind where the gears ride you want to keep clean somehow. Crud gets down in there and it's a battle to dig it all out. Anyone who has had a housing media blasted can relate.

Light surface rust it should clean up without too much effort. If it's dark scaly flakey type of rust with pitting too deep to get into it may need to come out and be dunked or soaked in something anyways.

If it's corroded to the point where the metal is potentially compromised you may just want to get a new housing and swap your parts over to it.