Could have sworn I posted this before... This is easy, just modify /etc/pam.d/sudo like
root@sleipnir /opt/ats # cat /etc/pam.d/sudo # sudo: auth account password session auth sufficient pam_tid.so . .
Obviously make sure you leave all the other lines in there, or you are in trouble. In iTerm2, you also have to turn off the Advanced setting named
Prefs > Advanced > Allow sessions to survive logging out and back in