The terminal at the Living Quarters will open using the Steam Battery, in the same way that you open Sully's, except that the connectors must equal -3 instead of -5.
To use the terminal, you need to get the key, which is far away on the right side of the island, in a closet at the Greenhouse of the Production zone (Botanical Research Laboaratory). You will need to get the Bridge Key from Captain Ziggs' quarters atop the Hub, and then go through the Research labs to find the key.
There are four essentials : get the vine from the top of the building left of the Living Quarters, reactivate Sprocket in Sully's, get the rubber mallet from Sully's, and get the Dirty Beaker from inside the Museum. You could also enter the Mayor's office, but only to get the code number, which is 0516.
in the trash
Enter steamworks island and go left. It's RIGHT THERE
Use it for the steam terminals
in the elevator there is a secret room with a skeleton that is where it is
on the trash can
it is in sully's steam powered paraphernalia
There are no ghost on steam work island
yes there are many bateries
The Steam Battery is in the garbage bin on the side of the Clockwork Cantina, which is just to your right when you enter the island.
You use the steam battery in Gear Alley. On number 5.
The Steam Generator (to open the doors) is in the trash bin to the right of the Cantina.
you have to get the number: minus five