SilverBullet
never slow down...you never grow old
Well, that and it dropped almost a volt without anything running.
But that is normal. A battery will charge up to a higher voltage but not maintain it. Same when your bike is running with the alternator input to the battery it will read 13.8-14.2 volts. But once the charge is removed battery will slowly drop to normal static voltage of 12.6-12.7 volts, never higher.
But just because a battery reads 12.7 volts doesn't mean it is good either. It could have a weak cell and not able to deliver a load. I was just pointing out that per your readings only the battery would be presumed good and not "bum" like you said. Since you bought the bike used and battery condition is unknown I would suggest to replace it. Not worth getting stranded over a $55 battery. Yuasa AGM highly recommended, YTX12-BS. Try and save a few bucks and buy the cheapo off Ebay and you're taking a chance.
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