Alternator help please

[Mick Rae]

Please excuse my ignorance in advance. I'm not home, so don't have my manual. And I'm not very learned about alternators!
I spotted a brown wire, not connected. The alternator was replaced a year back by a garage. The wire in question is not one of the thick browns that goes to the plug. It is a thinner brown, no trace. It has a spade type connector on end (see uninformative pic!). It looks like it us just right length and position to connect to a spade terminal located in plastic of rear of alternator, at bottom.. I can see that it has been 'modified' in length (made longer with new wire), and connects to the brown terminal of the starter solenoid. There has been some 'wiring mods' on car (previous owner).
With it disconnected, all seems to work. Ignition light comes on with key turned, and goes out as soon as engine starts. Runs great. All electrics work. Ammeter reads slightly (very slightly) into + when running at idle.
I should leave it disconnected and tape end up is what I am thinking. But any advice to contrary will be listened to right now! Esp as when disconnected all is good. I'm really sorry for being so dim, hope this is forgivable!

 

[Mick Rae]

Further info, I case it helps: Into the plug, on alternator, I have three thick brown, one with a black trace. All of these connected. The disconnected wire from starter is a thinner brown, no trace.
Could my mystery wire be surge protection thing perhaps (I'm googling, always dangerous combined with lack of knowledge). Would car run fine with that disconnected? Assume I should reconnect? Not doing anything for now though, will wait for expert input, going nowhere today anyway. Beginning to think that the mystery wire may be redundant for this new alternator (same as an MGB alternator) and I just haven't noticed it before now. Wishful thinking?

 

[Penguin]

It doesn’t sound like you have an issue especially it the amp meter show a bigger charge rate when you raise the rpm.

 

[classicalgreen]

my car had an alternator swap many years ago .has a 'spare' wire taped back on itself had no issues until other day when ammeter needle has decided to swing wildly .settle bit and again swing wildly. ? checking with volt meter shows battery oK and when running engine battery voltage fluctuates . so assuming my alternator voltage stabiliser /controller is on way out! have replaced regulator (£9) rather than alternator. running test and lights on/off shows all now well