Actually, all SR71s were two seaters (one pilot, one RSO). However, I think you're referring to the SR71 pilot training aircraft which is a totally bizarre looking variant.
Like I wrote "the LEAST rare SR-71 spy plane 2 seater", meaning the most common of the Blackbirds was the 2 seat SR-71(32 built), as there were more 2 seat SR-71s built than 1 seat A-12s(13 built, plus 2 M-21s and 3 YF-12 models being built-the YF-12 has no chines on its nose to allow a radar suite to be installed, this forced designers to include a single fin that is retractable under the fuselage as well as a fin under each engine nancelle)
The bizarre looking twin cockpit trainer aircraft was a SR-71B model(2 of the 32 SR-71s were built as dual control, elevated and offset rear cockpit B models). The SR-71B also had the ventral fins of the YF-12.
The A-12 trainer had 2 sets of controls, like the SR71-B. The A-12 trainer was called the "Titanium Goose.".
There was also an SR-71-C built which was the front section of the Static Test Article and the rear section was the back section of a crashed YF-12.
Pic #1 SR-71 trainer with raised 2nd cockpit slightly offset
Pic #2 YF-12A Interceptor notice the chine-less nose that houses the fire control radar to track AIM-47 missiles
Pic #3 Good pic of a YF-12A in NASA livery, notice the 3 ventral fins, 1 in the center, and 1 under each engine. Also carrying a "cold tube" experiment for NASA.
Pic #4 Pic of SR-71 C model, front is SR-71 test article, rear was a crashed YF-12A, so it has the fully chined front coupled with the 3 ventral finned rear fuselage This craft was nicknamed "The Bastard" as it supposedly yawed slightly during its high Mach cruise.
Pic #5 A-12 trainer with its dual cockpit, used to train CIA Pilots, no "Geneva Conventions" card for these Pilots, it was a covert mission, the SR-71 was the overt mission. This trainer retained the J-75 engines and maxxed out at Mach 1.6. Proper A-12's being the smallest and lightest of the Blackbirds also had the smaller fuel load of just 64,000lbs, the SR-71 took 80,000pounds of JP-7. One A-12 mission saw 94,780ft in altitude.