The "rust" may be factory preservative which is often a rusty looking grease.
Let soak for a day or two, apply more CLP then GENTLY scrub with a brass "toothbrush" to remove the loosened rust.
Wipe dry, then apply more CLP as a protective coating and to continue to "work" on any remaining rust.
Parkerizing is very rust resistant, but far more so if you keep a thin coat of CLP on the metal at all times.
I keep a clean nylon toothbrush handy. After using or handling the gun I apply a few drops of CLP to the brush and scrub the metal, which helps remove any rust or dirt and refreshes the layer.
After use I rinse the toothbrush in a solvent to clean it, then apply more CLP.
If the toothbrush is solvent proof, you can rinse in lacquer thinner or paint thinner to clean it.