If you are just storing,, use any oil that won't gum up, or ooze out, after time.
If you are cleaning for a new shoot, I recommend an automotive "Break-in" oil that is high in Zinc(ZDDP) to help reduce copper fouling.
Proven concept: Break-in oils show superior results over typical gasoline or diesel engine oils. Stock up your favorite brand now!
www.enginebuildermag.com
For the car guys on here,
https://bobistheoilguy.com/ has all the info you would ever need to know about automotive oils and fluids.
He has a very good forum as well as one section for firearms...
https://bobistheoilguy.com/forums/forums/firearms-lubes-cleaners-maintenance.38/
jm2c... Enjoy!