Fort Defiance was found by the dwellers, but its secrets - and especially the knowledge secreted away on the top floor, behind top grade military security - are not yet ripe for the picking. The dwellers need to gain a military ID in order be recognized as worthy of entrance.
Although turning the power on for the facility granted access to the Brotherhood wing, it's impossible to gain access without military credentials. That much is made plain when the players search the wing and approach the laser grid protecting the elevator to the upper floors.
Players need to attempt to register themselves at the Brotherhood terminal up on the third floor (from the bulletin board where the previous quest ended, that means going down the hall, up the ramp to the second floor, up the metal stairs to the third, and finally the terminal near the grid-protected elevator to the fourth floor). The system will demand a printed military-issue ID, which requires the player to first complete Back to Basic and then print it out at the Charleston Capitol Building, in the DMV.
Players have to enter the DMV, apply for a government ID on the terminals near the entrance, then take a number from the printer and finally boot up the department from the terminal in the center of the room. Department B is the right choice and will promptly spawn a horde of petitioners angry about the player's cutting in line (i.e. feral ghouls). Players simply have to survive until their number is called, then converse with the DMV Bot B2 to learn that a postmarked proof of Charleston residence is required. The mailbox is in the overturned house just outside the Capitol Courthouse.
At this point, the player will likely experience a bout of swearing.
The junk mail in the mailbox provides proof of residence, but it will not match the one provided in the application. The bot will request another form to compensate for the problem. The form can be obtained from the Charleston Capitol Courthouse on the other end of the building (or a short walk outside). The form is located at the bottom floor, in the Office of the Registrar, on the counter.
Returning to DMV Bot B2 will reveal that it's not qualified to process the form (as it's for renewals, not issuing new IDs) and will refer the player to Department C. This requires booting up Department C, which spawns a second horde of feral ghouls. Once it's fought off, DMV Bot C1 will finally converse with the player, only to ask for a coffee break. After it's over (just wait), it will sadly inform the player that it needs a birth certificate.
After a psychotic episode, the player needs to head over to the terminal on the west side of the room, near the Overseer's cache, and learn about the Error 34B/1 caused by the absence of the certificate. Fortunately, this only requires the player to head over to the governor's office and use the governor's seal to stamp the document and turn it in with the bot.
Thankfully, this will satisfy the bot's requirements. All that remains is returning to Fort Defiance to register at the terminal and gain access to the top floor. The quest ends when the player interacts with Wilson's terminal at the end of the hall to the left and reads the URGENT: Touchdown Recovery topic.