Thank you for the replies. I have not investigated yet as my Aircraft is away from home. On another forum I read the following
The alternator inop light works on the principle of opposing voltages or
potentials. The light is powered by a 5 amp breaker and at the same time by a
line from the ammeter shunt also protected by a 5 amp inline fuse. As long as
there is voltage on either side of the lamp the light is out. If the
alternator stops working the voltage from the breaker goes to ground and lights
the lamp. Use the press to test feature and see if the lamp glows brighter
while testing. There is a 30 ohm resistor going to ground in the Alternator
Inop light circuit after lamp and breaker. It is there to absorb the voltage
from the ammeter shunt if the lamp fails or to absorb some of the voltage if
the 5 amp inline fuse near the ammeter shunt blows.
So there are three likely possibilities. The 5 amp in line fuse is open or
there is a short circuit after the lamp or some other open circuit between the
ammeter shunt and the resistor. Some of the circuitry is also protected by
diodes to prevent voltage from lighting other lamps such as Vacuum Pump, or Oil
except when using the press to test button when all the annunciator lights
should light.
This opposing potential feature is pretty neat but a little unusual or at least
so in the way that Piper did it as there is no dedicated sensor like Beech and
some Twin Cessnas us
I’ll check out the inline fuse as wigglyamp suggests and for some reason I have a gut feeling that the the 30 ohm resistor might have broken down a little and started to short out. Let’s say the resistor has now partially burt out and is now 10 ohms? Would this explain why the indicator lamp gets slightly brighter when the TEST button has been pushed?
As part of the circuit diagram is missing for the OIL and VAC lamps I can be bothered to think about it anymore – I’ll get my pre-historic Avo 8 out – much more satisfying than using my plastic digital test meter and at least it make the plane’s circuits look modern!
It is certainly true that a lamp will illuminate only when there is a voltage across it 
I am not taking the p1ss – that is how everything in electrics works. You need a voltage (potential) difference for a current to flow.
However " It is there to absorb the voltage from the ammeter shunt if the lamp fails or to absorb some of the voltage if the 5 amp inline fuse near the ammeter shunt blows." does not make any sense to me. A resistor is not going to “absorb a voltage”. I think Cobalt (#5) has got it right as to the purpose of the resistor. But maybe there is something else…
A resistor is unlikely to corrode to a lower value. Corrosion normally eats away material.
Just in case anybody has the same problem I finally discovered the reason why the alternator light was permanently stuck on.
The inline fuse holder is actually located near the battery box and the soldered wire in the end of the fuse holder had oxidised and fallen out. The two ends that parted are marked by the red arrows Luckily the bare end with 12 volts on was lying on some aluminium near the battery box but had never shorted out to ground.
The break is marked on the circuit diagram with a red line below. The indicator lamp (for this lamp only) should actually be 6 volts but like on many Pipers a 12 volt lamp has been installed in the past by mistake. At present it glows only very weakly, if it was the correct 6 volt lamp an alternator failure would illuminate at normal brightness.
The reason why this lamp blows so often is that the “test” button puts + 12 volts on a 6 volt lamp. Best not to hold in the “test” button too long. It is a shame I can’t substitute the “OIL” “VAC” and “ALT” lamps for flashing LED’s – they would be a lot more obvious.
Well done on finding that.
This is a common problem in GA – just as it was on Vauxhall Vivas 50 years previously, whose electrical system build quality all of piston GA has inherited, with superbly waterproofed (not) connections
