WD-40

If the dead cylinder runs when you force it rich it must be a problem in the carb. When you cleaned the jets did you spray carb cleaner through the circuits in the carb body to check that they're all clear? The jets can be clean but the circuits are still blocked.

Good use of the technology

With the regulator rectifier unplugged you'll have no charging so the voltage will be whatever the battery voltage is. The battery will drain so don't go too far with it unplugged

I'd do as bender said when it cuts out check if it has spark. You could also open the drain screw on the carb and check if it's got petrol to the carb. Also when it's cut out check if it's got compression. If the valve clearance was too tight it could loose compression when the valve get hot

What part of the issue would that cause? And how would I go about testing it for failures when hot? That bit - Once the bike warms up, the idle drops, as well as the voltage reading - stays around 12V when it now idles at around 1.5k, and can drop further to ~9V when giving throttle - After a few rides, when coming to a long stop, the bike will cut out and the main fuse blows. I'd measured the output from the reg/rec when it's cold when you first start it up and everything is running normally. Then measure the output as the bike heats up and starts to fail. It's just a guess but worth a shot. Another way to test the theory would be to unplug the connector going to the reg/rec and see if the bike fails in the same way as before or runs normally. If it still fails then the problem isn't the reg/rec. If it runs normally then it probably is the fault. With the reg/rectifier unplugged the bike will be running off the battery so the battery will eventually go flat

Could be the regulator/rectifier failing when it gets hot

Nice one. You know what the next step is now......12V upgrade

It must be a bike that gets stolen a lot. Just in case you didn't know already the engines in those Gs aren't made in Germany https://www.bmwgroup-werke.com/berlin/en/unser-werk/internationale-produktion.html

I'd start by confirming the mixture screws are correct. A carb balance would be a good idea too. There's a manual. There's a voltage check for the TPS in there https://drive.google.com/file/d/0B28GkOK3QDM-RkVGdl95RXV4NEE/view

You need to check the AC voltage coming from the stator. Unplug the stator connector and start the bike. Set your multimeter to AC voltage and measure the voltage across all the combinations of the three pins on the connector. Measure the voltage at idle and 5000 RPM. All the combinations should show roughly the same voltage. It'll should be roughly 20V at idle and 60V at 5000RPM.

Try putting the choke on a bit. Does it pull away better or worse with the choke on? If it's better there must be a lack of fuel. The sr125 manual I saw says 2 turns out on the mixture screw. Try that. Is it better at 2 turns? You said you adjusted the needle position and it had no effect? If it had no effect that sounds like the main jet or main air jet could be blocked. If you move the clip down it makes it richer. Move it up makes it leaner.

I agree. Also if you don't know much about bike mechanics bring someone with you who does when you view it.

ebay? https://www.ebay.co.uk/sch/i.html?_from=R40&_nkw=125&_sacat=422&_fcid=3

There's a carb removal. He shows the choke near the end

I had the same problem. The bike would die during prolonged high speed motorway riding but run normally at lower speeds. The problem was the fuel cut off tap had corrosion in it on the vacuum side so it wasn't opening fully so the carbs would eventually run dry. Cleaning the corrosion out fixed it.

Here's a good manual on older Honda electric systems. You might find the answer in there. https://www.4shared.com/office/AJa2xPW2ce/Honda_Motorcycle_Electrical_Sy.html

That's dissapointing. How many miles on them? Are they Dunlop? Is the other one cracked too?

What's does the date code say?

fastbob mentioned in another thread about the cylinder head not grounding properly. If you've got a jumper cable you could clamp it from the head to the negative battery post or if you don't have a jumper cable you could take the spark plug out and join a wire to the threads of the spark plug to the negative battery post see if you've got spark with a good ground

Melted it? Try giving the cable a bit more slack and see if it stops slipping. If the cable is too tight it's the same as riding with the lever slightly pulled all the time.

I think going by the AC voltage measurement you can say the stator needs to be replaced. The voltage across A and B didn't really increase when you increased the revs to 5000RPM. It should increase and all three phases should be the same For your resistance measurement did you take into account the resistance of the meter leads? If you didn't, you should touch the two probes together and whatever reading you get take that away for your measurement.

Rubber parts tend to suffer over time so it'll probably need new tyres and maybe new brake hoses. You might find that the fork seals start leaking when you ride the bike for a while. The battery will have to be replaced. You should check the brakes are working properly, maybe give the calipers a clean. Check the condition of the chain. Make sure there's no stiff links. Give it a clean and an oiling. Do an oil change. Clean out the fuel system and replace the fuel. That's all I can think of. Your float height should be fine as long as no one has adjusted them in the past.

That's true. Just seems more likely that the chain would come off

I don't think a 2001 R6 has a hazard switch. He might have been trying to add one. A LED is a diode so there's no reason to be adding another diode to an LED. He's either messed up the wiring connections and joined the two sides together, or he's taken the indicator switch apart and messed it up or he's trying to add a hazard switch. I think as fastbob says whatever you've done take it apart and start again.