Well, it sounds like things are fine in the alternator department. How many grounds did you clean? There's something like 4 thoughsand of them. j/k, I forget how many there are... something like 14. Do a search and you'll find a few posts that show all the locations.

FYI, you should post the year of your car as it can sometimes lead us to an appropriate conclusion. It looks like you have an S4 from your referrence to the LH brain. It could be that the turn signals are impacting voltage to the LH brain thus causing your stumbling. But tough to test.

Another thought is you may also want to check the fuel pump relay. Here's my thought process. The flasher pulses, and if the FP relay is marginal, it could slowly degrade the fuel flow and hence result in a stubling idle. The headlights come on once and so the impulse on the electrics is one, giving the FP relay time to "recover". I'll bet if you sat there with the headlights on and turned them off and on several times like a turn signal, you would get the stumbling idle like the turn signal. If it does, then you would know this is a voltage problem and not turn-signal problem.

Another test would be to swap the horn relay with the FP relay (I think theres are interchangable). Try that and see if the prolem persists.

We're grasping at straws here, but hopefully this will lead you in the right direction.

Sorry I don't have anything more concrete

Ahh I see those details are not being posted in the signiture any longer. Well the car is a UK S2 1985 Auto.

Your right about the amount of grounds, but I know I did something over 10 maybe 12 so could be I missed one or two.

Yes the stumbling does get worse with the headlights on, as does it when I put the car into reverse, without flasher going.

And everything combined, i.e. headlights on, indicators on and reverse engaged boy it really starts to stumble.

Will try the fuel relay tip, and report back, Thanks.

You're not a member so you lost signature privileges. Pay the 12 pounds and join up. You know it's worth it.

Edit:
Just saw your post about the best money spent on the 928... Good job! Signature privileges should come back shortly.

Looking at grounds is a great idea since there are so many of them... but what about the + lead? It's very long, and could be causing the problem. If you can, run a DMM between the starter + terminal(the BIG one) and the battery +. If there is more than a few tenths of a volt measured across these two points at any time, you probably need to replace it. Also check connections at the jump post and the nearby 14-pin connector.

HTH