Low voltage = no charging
12v at the alternator doesn't necessarily point to the alternator being faulty. Remember, the voltage regulator is not a throttle valve placed in between the alternator and the battery. The alternator B+ (output) and the battery positive are electrically common. A faulty voltage regulator, faulty wiring or connections between the ignition switch and the voltage regulator, or faulty wiring or connections between the regulator and the alternator can all produce this symptom.
The system is really simple. Components are alternator, voltage regulator, ignition switch. Here's a diagram; your '71 car uses the electronic system shown on the right:
Check for line voltage at the blue wire going to the "top" of the triangular connector on the voltage regulator with key on and engine stopped. If none, fix the wiring between the ignition switch and regulator, and/or the ignition switch itself. If you do find line voltage on this blue wire, then check for continuity of the green wire from the voltage regulator to one of the alternator's field terminals. If none, repair the wire. Check for 0v (or minimal voltage indicating at least a passable commonality) between alternator B+ output terminal (the threaded stud) and battery poz with engine stopped. If you see 0v, your car is possessed or it is in fact charging and you're not measuring it correctly. If you see anything other than 0v, then fix the wire from the alternator B+ to the firewall main disconnect and the big terminal on the starter motor and the big terminal on the starter relay and battery poz.
If you find no fault in the wiring, that narrows it down to the alternator or the regulator. To test the alternator without removing it from the car, disconnect the wires from the "FLD" terminals on the alternator. Carefully run a jumper wire from the B+ ("BAT") output stud to one of the alternator's field ("FLD") terminals -- it doesn't matter which one. Then connect the other field terminal to ground and start the engine. Don't run it much above idle speed, for you are "full fielding" the alternator, taking the regulator out of the system, and if you rev it too high, the alternator can produce enough voltage to blow bulbs and cause other damage. If the full-fielded alternator gives you normal or near-normal light brightness, blower speed, ammeter reading, and (most importantly) voltage readings, then the alternator's probably more or less fine and the regulator becomes the prime suspect.
Be very careful with rebuilds. It's tempting to get the $24.99 "remanufactured" alternator from the parts store, complete with the "lifetime warranty", but if you want to do the repair just once, stay away from this indifferently-thrown-together junk. That "lifetime warranty" means you get to spend your "lifetime" swapping repeatedly-dead remanufactured parts under "warranty". Likewise, quality of generally-available regulators has been dropping. Get a brand-new Chrysler alternator and regulator from Old Car Parts Northwest, if you need either component. Unless you plan on upgrading the charging system wiring, specify an alternator of not more than 50 amps. See here for system upgrade info.
12v at the alternator doesn't necessarily point to the alternator being faulty. Remember, the voltage regulator is not a throttle valve placed in between the alternator and the battery. The alternator B+ (output) and the battery positive are electrically common. A faulty voltage regulator, faulty wiring or connections between the ignition switch and the voltage regulator, or faulty wiring or connections between the regulator and the alternator can all produce this symptom.
The system is really simple. Components are alternator, voltage regulator, ignition switch. Here's a diagram; your '71 car uses the electronic system shown on the right:
Check for line voltage at the blue wire going to the "top" of the triangular connector on the voltage regulator with key on and engine stopped. If none, fix the wiring between the ignition switch and regulator, and/or the ignition switch itself. If you do find line voltage on this blue wire, then check for continuity of the green wire from the voltage regulator to one of the alternator's field terminals. If none, repair the wire. Check for 0v (or minimal voltage indicating at least a passable commonality) between alternator B+ output terminal (the threaded stud) and battery poz with engine stopped. If you see 0v, your car is possessed or it is in fact charging and you're not measuring it correctly. If you see anything other than 0v, then fix the wire from the alternator B+ to the firewall main disconnect and the big terminal on the starter motor and the big terminal on the starter relay and battery poz.
If you find no fault in the wiring, that narrows it down to the alternator or the regulator. To test the alternator without removing it from the car, disconnect the wires from the "FLD" terminals on the alternator. Carefully run a jumper wire from the B+ ("BAT") output stud to one of the alternator's field ("FLD") terminals -- it doesn't matter which one. Then connect the other field terminal to ground and start the engine. Don't run it much above idle speed, for you are "full fielding" the alternator, taking the regulator out of the system, and if you rev it too high, the alternator can produce enough voltage to blow bulbs and cause other damage. If the full-fielded alternator gives you normal or near-normal light brightness, blower speed, ammeter reading, and (most importantly) voltage readings, then the alternator's probably more or less fine and the regulator becomes the prime suspect.
Be very careful with rebuilds. It's tempting to get the $24.99 "remanufactured" alternator from the parts store, complete with the "lifetime warranty", but if you want to do the repair just once, stay away from this indifferently-thrown-together junk. That "lifetime warranty" means you get to spend your "lifetime" swapping repeatedly-dead remanufactured parts under "warranty". Likewise, quality of generally-available regulators has been dropping. Get a brand-new Chrysler alternator and regulator from Old Car Parts Northwest, if you need either component. Unless you plan on upgrading the charging system wiring, specify an alternator of not more than 50 amps. See here for system upgrade info.