I don't know if/where you have a short. You'd be blowing a fuse if you had a short, normally, then again it's an old bike.
Couple things come to mind though:
- at somewhere between 2500-3500 rpm your charging system should usually put out 14+ volts as read *across the 2 battery terminals* with your voltmeter. So my question is -- was the bike in neutral and were you revving and holding steady at, say, 3000rpm when you read voltage across the battery? If you just started the bike and let it sit there idling then read across the battery, unless your idle is WAY too high (up around 3000rpm) -- at the normal 1000rpm idle, you will NOT normally read the 14 +/- volts put out by a motorcycle's charging circuit.
- if you think you have a short that is shunting your charging circuit output to ground -- I'm pretty sure the short would take the voltage down to zero, not from 14v down to an arbitrary level like 12v (or 11v or 10v, etc) -- a short just shorts the entire voltage to zero (and should blow the main fuse in the process). If you're not blowing fuses, you may not have a short.
- do your lights and signals work? if so, at least part of the wiring harness is fine
- I think the voltage regulator is the part of the electrical system that maintains the charging voltage at the usable level, no higher than somewhere around 14volts max at around 3000rpm.
- is it possible the battery is old and has an internal problem? 'Running rough' might be due to a low battery. If you have one of those portable jump-starters you could hook it up to the battery and see if the bike runs. If the 'running rough' condition goes away, the battery by itself is under-charged. If the battery is in okay shape (say, no white crusty cells visible) you could try trickle charging it then re-check the charging voltage with the bike revved up to 3000rpm or so.
- the neutral switch behavior you noted sounds like -- a SWITCH, ie. 'on then off' so I bet it's not the problem.
- it sounds like you put your test light *in series* between the bike's '-' battery terminal and the ground wire (the ground that is usually strapped to the engine/chassis mount point). Well, electrical current (electrons) flows between the negative side of the battery through the wires to the positive side of the battery -- that electron flow from one battery terminal, through the bike's wiring, and then returning to the other battery terminal is a circuit. If you think that, under normal conditions, there is no current (electrons) flowing between the '-' battery terminal, through the battery ground wire, and ground, that is a mistake. Why then would we need a wire from the bike's chassis to the '-' battery terminal if there was no electrical flow there. If there was no flowing current (electrons) between the battery's '-' post and the black wire connecting the post to the bike's chassis and engine, then there really wouldn't be a circuit -- you'd only have the '+' battery terminal. But that's not how it is.
It sounds like you removed the ground strap from the '-' battery pole and used your test light to connect the '-' battery pole to that ground wire -- in that case your are reading CURRENT IN SERIES and you should get a reading. If no current flowed from the '-' battery pole in the ground wire -- then you wouldn't need a ground wire -- nor the '-' battery post -- but you'd also have no circuit on the bike.
If your battery is ok, and then fully (trickle) charged, and you do not get 14volts at 3000rpm read across the battery terminals -- might be a bad voltage regulator. *Might* be.