Fairly certain it would be the manual lever assembly then.
As far as I know, manual and automatic operation signals go down same wires from front of car to rear brake unit. Manual works so loom to point of the signals splitting is okay. There is a connector under the passenger seat on which could be an issue but would I believe affect manual and auto
Auto release is conditional on throttle and being in gear, no need for clutch signal as when in gear an auto is sitting on it's fluid flywheel.
Auto on has no conditions AFAIK
except engine off.
Car starts okay and reversers work so gearbox selector switch okay. ie conditions met for auto off.
I believe the auto signals and manual signals come together at the manual release on the dash.
There are tales of replacing that and problem solved but sparing on details
So best guess.
I've put some detail behind the guess in the hope someone else will tell me I'm an idiot and there is something less expensive to check.
Switch units relatively cheap second and so may be worth a try.