check the voltage but my digital meter was all over the place, not readable at all.
I bought a $3 voltmeter (digital is all they have) and got the same gibberish, IE. not readable. How does one read the voltage on one of these old bikes?
Most likely cause is neither meter has emi (electro magnetic interference) protection;
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running engine on an old British bike, HT is tens of thousands of Volts, usual source of emi.
You should not have to spend much on a meter to get emi protection, but three bucks is probably too little ... Just make sure whoever sells you your next meter agrees it does have the protection. Also ensure any new meter has good calibration - it should measure 12.6V connected across a well-charged lead-acid battery, including AGM and gel; higher is not better, it is poor meter calibration, which makes it harder to use its returns for fault diagnosis.
Also Voltage with engine off was ~11 and with key on <10.
The battery is very flat, in need of an overnight trickle-charge at least; remember trickle-charge should not be any more than one-tenth of the battery's Amp-hour rating; i.e. if the battery is 10 Ah, it should not be charged any faster than 1 Ah. If that doesn't get the battery up to ~12.5V with the key on, you need a new battery.
I am convinced that voltage is unregulated
Mmmm ... like tightening head bolts with vise grips and being "convinced" they are torqued correctly?
corroded connections (obviously on the Diode).
Possibly ... Lucas and Triumph (and BSA) did the oif Zener ground path very poorly.
Zener in the standard OIF position, you will have to remove the timing side sidepanel and air filter, Zener is mounted in the leading edge of the air inlet (it is mounted on the airbox to save the cost of the dry frame heatsink ...
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). However, it was either Friday afternoon or the designer was on a promise that night, because the (original) return is the ring terminal with multiple Red wires attached to a battery carrier bolt; Lucas had done this better on the dry frame models for years so who knows why this was signed off.
As you are in there anyway, wise to unbolt the Zener from any mounting, clean off any corrosion on the side that goes against the mounting, the mounting itself and the Zener's thread. The Zener's side needs to make good physical contact with any heatsink, you can buy special heat-conducting paste, that'll also ensure corrosion does not reform ... or I have always used graphite grease, that is also useful for other things ...
You can take airbox and battery carrier to pieces, scrub off any corrosion where they and the Red wires ring terminal are in contact and reassemble it (with smears of graphite grease between?); around San Diego and similar, corrosion probably won't be a problem for some time. Otoh, if the Zener is not being made redundant by a reg./rec., I prefer to: drill another 3/16" i.d. hole near the Zener, make up a Red wire to go from the hole to an existing Red wires snap connector, 3/16" i.d. ring terminal on one end of the wire, bullet on the other end, connect the ring terminal to the airbox with a 10-32 or M5 bolt or screw and nut, bullet in the snap connector.