If there was no higher voltage, i.e. the 14volts at higher RPM, I might suspect voltage regulator or external wiring for alternator.
Alternator works like this
When you turn on the key the Battery Light will come on, this is an important circuit, it is sending the Voltage regulator "startup" voltage.
Voltage regulator sends 7 to 9 volts to the brushes/slip rings, this powers the rotors wiring to generate an electric/magnetic field
When alternator starts spinning(engine starts) this 7 to 9volts creates a 13-15volt output from the 3 Field coils in the alternators case.
Once this 13-15volts is being produced the voltage regulator switches over to internal power and the Battery Light goes out/off.
An alternator can't start producing power unless it is given that startup voltage.
And if you just left alternator's rotor power "ON" 24/7 then battery would drain when engine was off.
1 wire alternators use an RPM ON/OFF, the rotor/voltage regulator gets "startup" power from the alternator's B+ hookup to battery, 24/7 12volts, but RPM switch inside cuts off the 12volts below a set RPM then turns it back on above a set RPM.
No battery light circuit needed, and no battery drain when engine is off.
It does surprise me that your battery light is not ON at lower RPMs, does it come on with the key?
Voltage regulator monitors system power, it is set to maintain about 13.5volts when battery is fully recharged from starting, just after starting battery is drained and voltage regulator will increase system voltage to above 14 volts, but stay below 15volts.
It adjusts the output voltage by varying the input voltage to the Rotor brushes, the 7-9volts, 9 volts to rotor would produce higher output voltage.
So say you were at idle lights off, and battery voltage was 13.5v, when you turn on the lights that 13.5 volts would drop momentarily and then come back up to 13.5v, that's the voltage regulator responding to the extra power needed by lights on and it is sending rotor more volts to bring voltage back up to 13.5v.
When you increase engine RPMs voltage would go up so voltage regulator would start sending less voltage to rotor to maintain that 13.5v.
A 100amp alternator can generate 100 amps at high RPMs, that is it's Maximum power output, at idle RPMs it can only generate about 50% of that.
That is with 3 working fields, when a field fails then you lose 1/3 of the power generation.............BUT, voltage regulator just turns up the rotor voltage to compensate for the lost power generation, but at idle RPMs you would still notice a drop in voltage. i.e. head lights dimming.
When 2 fields are lost then you get what you have now, you only get voltage above battery voltage, 12.5volts, when engine RPMs are high, and it would be above 14volts because voltage regulator has maxed out Rotor voltage because battery is drained by running all the electrics at lower RPMs, i.e. just like after starting engine drain.
It could be just the diodes that have failed, and on most alternators you can change those, and the voltage regulator.
But I think you are right in changing out the whole alternator, the second most common cause for alternator failure is one of the bearings for the rotor goes bad, and putting money into the electrics of 22 year old bearings is not money well spent, IMO.