If any vehicle 'EATS' battery, then you have a problem on charging system....Alternator, or Regulator/Rectifier,....or you may have a current draw problem, when bike not running.....and you find that out by connecting an Ammeter in series with battery terminal...any. It should not be more than 30 milliamps. Or 0.03 amps
Have never run a GSX-S w/out a battery.......but have done it on another older bike. The bike ran, but revs were dancing all over the place, and the reasons was the battery acts as base- line provider of electrical power......meaning you have to rev the bike for these alternators to provide power enough for ignition....at idle is just not enough by itself....and battery supplements
You test the alternator by doing the opposite you suggested. .......by disconnecting the alternator, and running the bike ONLY on battery, or jump starter.........then reading the voltage on all three phases.....this is AC power, not DC.......Repeat.this is AC power, not DC before the Regulator/Rectifier.....and at 5000 rpm should be 65 VAC.
Easiest ways is simply reading voltage on battery terminals at 5000 rpms. It should be above 14 VDC to be capable of charging battery.
Manual also has resistance tests on phases on the connecter.....0.12 to 0.12 ohms
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