One piece of evidence to support two engine rooms that I don't believe I've ever seen mentioned, possibly because it requires a bit of a logical leap that may be a bridge (

) too far:
In "Space Seed," we clearly see that Khan and his men have, logically, seized (an) Engineering. They cut off the bridge's life support systems from there and capture and incapacitate Scotty.
Of course, near the end of the episode Khan somehow "closes [the] line" to "the Engineering section," preventing Spock from flooding it with gas, and goes there, where he starts an engine override and coolly figures out how to hack into the intercom system (thus learning that Kirk is coming).
One problem: none of Khan's men and women are in the room. The Enterprise seems to be in flight at least when Khan "discards" the Botany Bay, so abandoning Engineering is strange. And even if the ship isn't moving, I would think that a group of brilliant strategists would maintain a presence in Engineering regardless due to its clear strategic importance. After all, they were controlling a crew that, while not as strong and fast, was still about four times their number and knew the ship better. Given everything that can be done from Engineering - including cutting off life support to the bridge - leaving it unoccupied is odd.
And of course my solution is to conclude that Khan's men did stay in Engineering - in the primary hull. Khan, however, fled to the secondary hull. Good thing he noticed that the deck plans included two engine rooms.