Is this normal for these cars or maybe the alternator is going bad or maybe a wiring problem?
Do you mean the standard Mustang ammeter or an add on one? The following assumes you are talking about the the standard ammeter gauge.
No, it is not normal. I would guess an electrical problem since the stock 'ammeters' are pretty useless. They don't tell you much about what the alternator is doing.
A real ammeter is wired so that all the charge/discharge current is measured directly. That takes bigger wires than Ford wanted to pay for. If this car is wired as original the ammeter is essentially measuring the voltage across a 2 foot section of 12 ga wire between the alternator and the battery. In EE terms its called a shunt. That allows the meter to use very small wires and saved Henry a few $$. It is an ammeter, but the scale is so huge that the needle will barely ever move. It takes like 230 Amps to peg the needle in either direction and that is nearly impossible to do unless you have a massive short that you could find more easily with a smoke detector.
If you are seeing the needle and the lights both flicker I would say there is a loose connection or short in your wiring. It likely has nothing to do with the alternator. The reason you don't see the flicker in the other gauges is that they are extremely slow acting and you never see the effect. The ammeter responds quicker and lets you see the problem.
Do the lights flicker by getting brighter or by going dim? If it were a true indication of charging, a needle flick to the right would say more alternator output and the lights should get brighter. If the lights instead get more dim then its almost surely a wiring problem.
If there is actually a charging problem I would suspect the regulator before the alternator. The alternator is pretty simple and dependable although not a very high output. The regulator has a bunch of mechanical switches that can easily burn and not work well.