W-2 Division consisted of mainly FTBs (Fire Control Ballistics), who worked on the Polaris Missile System Fire Control Computers which were mainly digital and FTGs who worked on the Torpedo Fire Control System. This was mainly a Fire Control Computer (Analog/Digital Hybrid), on a Boomer, and at that time period, it was most likely to be a Mk 113 Mod 5 Fire Control System.
There were also MTs (Missile Technicians) assigned to W-2 as well. I believe they did something with some type of navigation system in the missile, but not sure. I think the anagram for their equipment was PORRI/POTS or something similar.
Basically, the FTG's job was to go down on the Boomer, run PMS tests (Remember Preventive Maintenance Systems?), on the Torpedo Fire Control System Mk.113 Mod 5, and if they failed, assist the Boomers' FTG crew (usually two FTGs usually 1st or 2nd class, sometimes an FTC) in repairing their FCS. When something was really down, and their period alongside was short, this may well have meant 24 hour days.
I would go into deeper detail about the system, but as you know, most of it was classified secret and probably still is. So I will just describe a generic overview of what a Fire Control System does and is. A Fire Control System consists of a Fire Control Computer as well as those input devices necessary to plot courses relative to ships motion and bearing as well as the projectiles' (whether it be a torpedo, missile, or a shell).
Basically the computer portion accepts the target ships bearing, speed, and range and your ships target and speed, and computes what is called a Fire Control Solution. In other words, what bearing and speed (In the case of torpedoes) or what bearing and elevation (in the case of guns) should the projectile be fired.
While other duties varied greatly, and probably varied with the ship -- such as missile entry security watches, or Damage Control Office watches.
As for working parties -- an FTG3 or even an FTG2 wasn't much rank in the FT Shop, as almost everyone is a petty officer - almost no E3's or below - so generally, when we got tapped for working party "volunteers" our petty officers went out on the same working parties as seamen in other divisions. I remember I often outranked the Boson's Mate in charge of the working parties by one or two ranks. Sometimes even First Class went on working parties, although Chiefs were pretty much safe.
Fire Control write-up by Jim Kloska - (a shipmate of the Webmasters, by the way - though it took me a while to figure out who this rabble-rouser was (!) Jim served on USS Proteus AS-19 twice, About 9/67 to 9/68 and 10/71 till 9/72 -- and also served on USS Hunley AS-31 from 9/68 to 10/71.