Although Joe Flynn's character is listed as "Captain Wallace B. Binghamton", his character's name in this episode is clearly "R.F. Binghamton", as evidenced by the sign at the entrance to his Quonset hut office.
The exact location of the island of Taratupa is never explicitly stated; but during Ensign Parker's first meeting with Captain Binghamton, Binghamton points to a location on a wall map and tells Parker "here is the Navy's real enemy". The location to which Binghamton points is southeast of Stewart Island (Rakiura), New Zealand.