If you suspect the rectifier it's easily tested using a simple multimeter.
Connect the meter red wire to any of the three yellow wires, the black wire to the red wire. You should get a meter reading of a few ohms, if any at all. Now reverse the connection & there should be a reading of infinity.
Once you have checked in this way, then connect the red lead of the meter to the green (earth/chassis) lead, & the black wire to any of the three yellow wire. You should get a reading of a few ohms, if any at all. Do this to all three yellow wires.Finally, do a check across the red & the green, once with the red of the meter connected to the red lead of the rectifer with the black lead of the meter to the green of the rectifier. Check for any resistance other than infinity. Now reverse the meter leads...again there should be no reading.
For the regulator you will need a variable voltage supply across the input connections white & green/earth/chassis. Then, using a multimeter set to DC volts with the range set to up to 25vdc, connect between the black & the green, the black being the regulated +12dc output.
Now set the input volts to about 13vdc...& check that the output voltage is the same. Then increase the input volts until the output volts reading stabilises at the preset voltage...this is normally set by the factory. If the output voltage rises at the same rate that the input voltage rises, then there's a problem somewhere. There're adjusters for where the regulator switches, but I no longer have this information, which is normally found in Haynes or Clymer manuals.
If you are wishing to save space under the seat, i'd go for one of these...
http://www.electrexworld.co.uk/rr24-regulator-rectifier-604-0.htmlIf you wanted your units tested, i'd be willing to do this for you as I have the relevant test equipment.