[swifty2014]

If the battery can't hold up when under load it is bad internally - maybe a weak cell. Replace it first then see if the running problem is any better.
I remember many times testing car batteries that the ones that stayed over 12.9 volts at rest, after getting a good charge seemed to be the ones that failed the load test afterward.

 

[swifty2014]

Are all the battery cables ends clean and tight? And engine ground?
Jump it with a non-running car battery and that eliminate any low battery crank amps.
That way you can go compare results.
A new battery can require a good slow charge to get up to full potential.

 

[swifty2014]

Some of the guys with the same type bike might chime in, but it seems like a small battery to me.
Do this test with a meter on the battery=

Put your meter across the battery and see if at rest it is at least 12.5 volts. May need a charge first.
Then watch it while you crank it for 10 seconds and it should be above 9.5 to 10 volts.
Then while running see if it can stay up to 13.5 to 14.5 volts as you rev it above 3000 RPM.
That will tell the basic health of the battery and charging system.

 

[swifty2014]

Find the connector for the famous 3 yellow wires, on the wiring that goes from the stater to the regulator, and look of an overheated connector. It may be that the charge system is going low when you rev it.
The 3 yellow wires can cause that if one or two of the 3 phase alternator has bad connections.
If it is burned, we cut it out and solidly connect them.
Unplug and reconnect all the other connection points on that system to see if that helps the connections.

 

[swifty2014]

It may be discolored from heat or be really obvious=

 

[swifty2014]

It may be dielectric grease put in there.
Otherwise yes cut out the connector and splice directly for the best connection.

 

[swifty2014]

You have to take the switch apart to see the sliding metal contacts and clean them.

 

[swifty2014]

Are you talking about the single brake light on the fender doesn't work?
If you mean the two lamps with the turn signals in the rear, they do no come on as brake lights from the factory.
Only if someone has modified the sockets.
The front ones do have a dual filament bulbs and are running lights and turn signals.

 

[swifty2014]

If you have an old cig lighter you might take out the spring and it may be small enough.
Cut and stretch as a temporary repair maybe?

 

[swifty2014]

My old 1983 is running richer since I fooled with the pilot jets, and it burns some oil.
My plugs looked like that most of the time, so I went to one step hotter to help keep them cleaner.
They were usually #8 so I went to a # 7 which is hotter in foreign plug heat ranges.
And yes the left rear plug gets crustier than the right rear. Same cylinder !
Must be the way the spark flame front flows?