When I was in I believe even the fact that you HAD a security clearance was not to be divulged to anyone after separation, let alone the level of it.
My wife worked for a defense contractor for years as a computer engineer. I do not know what she did. When I asked she always said, I will tell you when I am dead. I quit asking. They paid her well. Often she went TDY. Sometimes she went TDY and I did not even know where it was. At that time she was just a cell phone number.