You're right, two distinct engine rooms. My question would be then; is there any point in having an independently controllable secondary hull in TOS? The weapons are all on the primary hull, so it would offer no tactical advantage and the primary hull has more than enough room for the entire crew to serve as a lifeboat. So would there be a reason to have a crew there to pilot it after a saucer separation?
I believe that the TMP Enterprise has the same phaser emitter placement as the TOS Enterprise so the Engineering hull should have at least 4 on the bottom and 2 in the aft section, just above the shuttle bay. At the very least, the Engineering hull could shoot at whatever might be chasing it
As to crewing the different hulls - it would depend on the circumstances.
Example: In "The Apple" they would've abandoned the engineering hull and flew out of their with just the primary hull to try to escape with the lightest mass since the antimatter pods were rendered inert.
Or the impulse engine could be damaged like the Lexington's in "The Ultimate Computer" and then hypothetically the primary hull damaged and uninhabitable forcing the crew into the engineering hull and maneuver on warp drive alone...
In anycase, the Bridge, Aux Control Room in the primary hull or the Emergency Manual Monitor and Engine room in the Engineering hull could fly the ship as the circumstances dictate...