I think the other end of the red wire got cut off.

 

It is difficult to follow and interpret the pictures.
I looked at them multiple times and noticed a twin tuner II.
It looks like it might be part of interface for twin tuner II.
Consider review of online instructions for twin tuner II.

 

You can see that wire coming out of the twin tuner plainly.

OP why not call the manufacture to be sure. We're all just guessing as to what it is.

 

Here is the manual

As Todd1113 says above, this could very well be the power wire. Manual says red/green wire is power.

 

Thank you. I will look at the instruction for a twin tuner II.

 

Does the bike start up and run normally? If so, tuck that wire up under the tank and ride.

If not, figure out what its for and fix it.

 

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According to the instruction manual, it's a PC Link wire. Just neatly coil it up with a zip tie so it won't get damaged...

 

I keep my battery plugged to a trickle charger because I don't ride it often. I'm testing out the conditions. The battery is charged and it starts fine, but seems to die after about 5-10 minutes. I'm not sure the battery is charging, which may have nothing to do with the little red wire.

More testing required!

 

Good to know. I should just re-zip tie the cable and leave it be.