If you choose to find the diagnostic scanning module, you must go to the heavily irradiated and ghoul infested Vault 34. You can find the vault north-northwest of the NCR's Camp Golf or east of the NCR Sharecropper Farms near New Vegas. It is recommended that you bring a good supply of RadAway and Rad-X. There will be golden geckos on the way in as well as the ghouls inside.
Simply go to the room marked 'Clinic'.
As you walk in take your first right to the stairway that will take you to the 'cafeteria'.
Drop down the hole, exit the room and turn left.
Follow the corridor (and signs for the 'clinic'), until you see the room marked 'Clinic'.
The Auto-doc is on the back wall. Interact with it and the option to take the item will appear (you can turn around the way you came to leave after this if you are only here for the Auto-doc).
Attempting the surgery without the required Medicine 75 or Luck 9 will result in Caesar's death. You must then have either Medicine 50 or Speech 50 to explain to Lucius that Caesar's age was a complication in the procedure, or he will become hostile (unless your reputation with the Legion is "Liked" or higher).
In all versions of the game, the broken Auto-doc is in the clinic in Vault 34, not Security Station A.
You will not be able to offer Arcade Gannon as a slave if you recruited him after you have spoken to Caesar in private.
If you attempt this quest after losing Arcade by betraying him in For Auld Lang Syne, sometimes you can still get the option to sell him into slavery, although this does not seem to complete the quest. There is also no mention of him in the ending and he does not actually appear in The Fort.
The title of this quest is a play on Julius Caesar's famous last words,"Et tu, Brute?", from Shakespeare's play Julius Caesar which translates to "And you, Brutus?", showing Caesar's dismay in seeing Brutus taking part in his assassination.
The quest is an elaborate allusion to Julius Caesar, who did indeed suffer from an ailment that caused severe headaches and was also a secret from the public. Caesar's headaches were more likely to have been caused by a motor function disorder, causing him to fall regularly ("falling sickness").
If after Arcade is given as a slave the player speaks to him and says "The world needs Caesar more than it needs you" Arcade will respond "Victrix causa diis placuit sed victa Catoni" which can be translated as "the victorious cause pleased the gods, but the conquered cause pleased Cato." This is a quote from the Latin poem Pharsalia by Lucan, in which the historical figure of Caesar is portrayed as the main antagonist, and the main hero, the historical figure of Cato Uticensis, is eventually forced to commit suicide, being unable to defeat Caesar.