Is the other vac pipe connected - the one which goes from the right hand side (looking from the front) stub at the back of the manifold, and connects to the hot / cold air flap on the air box? If this is left off / is split / is connected at the back of the manifold but open at the other end (eg if someone has put a K&N cone filter on it but not blocked off the end) then that will cause a big air leak, leaning the mixture. If you leave the ECU vac pipe off, that should cause an over rich condition, as the ECU thinks the lack of manifold vacuum means that the engine is under a heavy load. Just wondering if you have an air leak from the other pipe, which coupled with the over fuelling you get with the ECU pipe off, balances out and lets the run car reasonably OK. If there is a leak at the other pipe, then with the ECU vac pipe on, the fuelling would be very lean indeed.
Now, usually with the other vac pipe off (and a big leak introduced) but the ECU vac pipe connected up properly, the idle speed woul be quite high, however it's possible somebody has adjusted the stepper motor idle screw to compensate (assuming my theory about a missing / leaking 'other' vac pipe).
Can you confirm the existence / condition / connection status of the other pipe? (if original it is a Red pipe which goes from the back of the manifold to the air box hot/cold flap valve, then there is a yellow pipe which goes from the other side of the flap valve to the flap actuator on the underside of the air box).
Lastly, assuming it is all plumbed in, is there any chance the pipes are swapped on the back of the inlet manifold? The ECU one (which goes to the fuel trap first as you know) should be on the stub on the left (looking from the front) and the hot/cold flap one should be on the right hand stub (again looking from the front). Not sure, but I had a feeling that one was a restricted pipe stub whilst the other wasn't. Might make a difference.
Of course, there are other places that you could get a vacuum leak, such as the breather pipes which connect to the front of the inlet manifold, or even the servo vacuum pipe - that could create quite a big leak, which again I could imagine could be countered by overfuelling by leaving the vac pipe off.
Just some thoughts! I can't imagine the car would run very well though in such a situation, but I've never tried it so you never know!
Edited by spiguy, 11 January 2016 - 10:36 PM.