[kz1000st]

You might check the charging system first. It could be the original battery that came with the bike. I don't recall Rich ever mentioning a battery change. I have a battery in my garage that I bought cheap. If I left it in the bike for a few hours off the charger it wouldn't start the scooter even though it read 12.5 volts. I bought one from NAPA and put it in. It will hold its charge for weeks and reads 12.75 volts. To me that was indication that the cheap battery had volts but low amps.
When you start the scooter your volt/ohmmeter should read over 13.5 volts with it running across the terminals. If you're having a voltage drop at the battery simply because you tried to start it I would think the battery is bad.