If I understand stand your question better this is what I believe will solve your problem;
I took a look at the Biketronics TATAN wiring color arrangement and most likely the RED cable is a straight (+) 12 Volt battery cable.
a. The blue in most cases is your switch (+) cable and your options are Deutsch accessory or the continuous on the radio (snap connects, solder & shrink tubes linking plugs/shoes)
b. The black is a (-) ground cable
c. There are the RED and WHITE audio RCA cables. They should plug into the stereo most likely connect to the pass-through adapter that they supplied
d. And your WHITE AND WHITE/STRIP and GREY AND GREY/STRIP speaker cables. You will need to connect directly to the speakers positive and negative phrase using snap connects or solder & shrink tubes
e. If you have the install kit Multi-Band or Sony should have a diagram wire sequence sheet
f. They do not show it but the RED and WHITE audio RCA cables most likely plugs into that orange module, which has a plug for their stereo.
g. That ⅛ mini stereo plug is an audio plug for the stereo.
h. You will need the install kit for this amp, which should have come with the radio.
If you do not have a Sony system I am not sure how to get the audio out of your system without that wiring harness or the ⅛ mini stereo plug. You have already spent a few bucks.
On the other-hand UNIQ Cycle Sounds at
www.uniqcycle.com can fix you up with a 300 watt amp that is 150 watts per channel for $50 sale price they also have the 400 watt amp and accessory kit with everything that you need; your missing link! You can call them as find out if they will sale the audio RCA converter module separately. If Biketronics sent you this module you can use any stereo. ZIP tie the two inside the fairing and you are in business
I personally have the 300 watt $50 amp on my serk and it works very well. I blow a 150 watt amp and we flip-flop for a new one with no problem. Small company great people and they will answer your questions. The only problem sense they are small leave a message, they will return your calls.