Boy you have got yourself into a pickle messing with the instrument cluster. The lights should come on when you turn on the key with the engine stopped. All of the circuits are close to ground and the lights burn. As each sensor opens the light goes out. The oil pressure light,

etc.

The alternator circuit light stays on because there is no opposing voltage out of the alternator to ground. In your case you have lost the ground on the alternator and/or regulator system or the wire from the bulb to ground is broken. Bulb out.

The light has nothing to do with the charging of the battery. It just indicates nothing at all coming out of the alternator, when lit. It won't tell you anything more than that. Thats why they call it an "Idiot" light. The alternator can put out just a little bit and that light will go out.

One diode of the three can go bad (open or short) and the alternator will charge only enough to keep the battery up during the daytime if it is driven long between drains. A bad diode can short and drain the battery too! There is no way for the regulator to know how much the battery needs without good connections. The regulator controls output of the exciter diodes to increase the field winding (magnetic flux) to control total output of current to the battery by watching tenths of a volt change in demand. 13.5 to 14.2 is its operating range. A volt meter tells you all you need to know about how it is working and to keep it all working good.

As far as the instrument cluster goes there is one wire that you think came off the cluster. Well to the best of my recollection that wire is an extra, it goes to nothing! If there is not a single spade, or round pin, to put it on, its a freebe!

Take the alternator off and take it to a parts house and have them spin it up and test it. It cost nothing because they have you in there hopefully to sell you one! Check for bad connections or broken wires in the tear down process. Good Experience to get to know your car! If you dare its not hard to check the brushes as a fellow brickboarder recommends Its usally about a ten dollar fix. Pass that get a rebuilt from a good supplier.

Also, judge how old the battery is, sometimes they short and take out diodes! Just in case it is that bad a fix!