If you ever restored an old baseball or softball mitt, there's a dressing that you can get to restore the leather. Sporting goods stores normally carry this stuff next to their mitts or bats. Since the grip is new, applying a very small amount (2-3 drops) may help restore the feel.
I've never tried castor oil, but have tried vegetable oil. Seems to work, but turned slightly rancid from sweat. Wondered about using linseed oil.