I had a pretty similar sounding thing happen a while back, it was sticky contacts in the starter solenoid. When you say "the bike still sputters and spats", did it sound like it was cranking over on the starter?
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That is exactly what happened to my ST4. Though it sounded like it was running it was just the starter not disengaging and kept cranking. Tried the "in gear, brake on, clutch out" but it still kept cranking...I had to wait for the battery to drain.
Got a new starter solenoid (don't remember from where but it was for a Kawasaki and had a different connector type), installed it and problem solved.
I have read the same thing quite a few times, seems like it might have been a typical problem on Ducks of a certain vintage. My ST4 is a '99'.