Thanks Bush, I did get a manual with the bike and just getting started on reading thru the forum to see what I need to be checking along with the stuff I would not think to check. Before posting to this thread I called my local Honda store and talked to the tech and he is thinking rectifier but said he would need to diagnose, just to get me up and running cause I want to trust the bike and get a feel for it( I have rode it 6 miles total). After ATVs for the last 15 years this older ST is a lot more complicated. I appreciate the information and answering my question, As I told Don B I just did not want to start another alternator thread.
You could save yourself the dealer's labour charge for troubleshooting this quite easily, since you confirm you have the manual. The only alternator test not shown in the manual is the dynamic AC output test for each of the three alternator coils. This tests the actual AC voltage being put out from each winding and is measured by disconnecting the red 3 point connector that runs between the alt and VRR, while the engine is running and comparing the AC (not DC) voltages between the three yellow wires. All should read somewhere over 25 volts AC and also all should be within a few volts of each other. Your test probes are placed variously between the three wires, on the alternator side of the connector, of course.
My previous '95 model alternator showed good on all the tests in the manual, even though I was only getting about 13 VDC at the battery. The dynamic test showed two coils at 25 volts AC, but the third at only 18 volts AC. This led me to believe that one coil had suffered some melting of the insulating wire resin somewhere in that coil, which did not produce a short to ground, but did reduce the output potential of that coil.
Given you just bought this bike, shame on the previous owner if he knew he had a charging problem before he sold you the bike.