Just a thought, but is it possible that aux. control could somehow be tied-in with engineering? It doesn't appear to be physically located within engineering itself because we can see the main corridor just outside the red doors.
However, in "And The Children Shall Lead," Scotty is doing an inspection round inside aux. control which is occupied by two red-shirted, engineering technicians.
Why would the chief engineer be monitoring aux. control if it wasn't associated with his department? Since Scotty spent most of his time in engineering, could this mean that aux. control might be located within close proximity to engineering, thus, suggesting a location within the engineering hull?
A possible hole in this argument would be "The Way to Eden" where a gold-shirted crewman is sitting at the control monitor in aux. control when Sevrin and one of his hippies enter in and sneak up behind him.
This would suggest that aux. control in nonexclusive to engineering personnel and may be monitored by other crewmembers, also. In this case, aux. control need not be located in the engineering hull.