Frequently starting your engine and then running it for less than 30 mins at highway speeds/revs is a pretty sure way to kill
any battery eventually, but especially so for the battery on a power hungry Spyder, and
EVEN MORE especially so on a V-Twin Spyder with a magneto charge system (like yours) that keeps a little stepper motor running for
30 odd mins after shut-down to hold the throttle bodies closed & avoid all sorts of nasty things!! :yikes: So that tone you hear for about 30 mins after shutting down the engine is normal & actually desirable - it's keeping you/your bike safe! :thumbup:
Still, it sounds likey you've already hammered your new battery into submission! :banghead:
But there's more - most new batteries
DO NOT COME PROPERLY CHARGED!! They get enough charge to show better than 12 volts, sure; but with any new battery, unless the seller you trust has told you that they charged it on a proper charger for
at least 12 hours BEFORE giving it to you, that battery will need a
PROPER charge of
at least 12 hours BEFORE it reaches full charge capacity and can then withstand
just a few of those '
start & run for nowhere near long enough' cycles!!
So hopefully, if you haven't killed your new battery, then maybe it can be saved by charging it on a proper charger for at least 12 hours (& not just on a low/trickle charge rate tender either - that'd need
even more charging time!

) before trying to start your Spyder again. And once you have a properly charged battery, you really should try to avoid starting your Spyder for anything less than a 30 minute run at highway speeds/revs! Anything less than that will have sucked more power out of the battery than it'd put back during any shorter run time/lower revs! Even just turning on the ignition to release the elec park brake (if fitted) will run that stepper motor for 30 mins & help drain the battery PDQ; and these things really don't like that!! So
unless you're going ryding, DO NOT START YOUR SPYDER - don't even turn the ignition on unless you absolutely must!! And if you go ryding, make it worth your while - 30 minutes as a minimum is a good start, preferably at highway speeds &/or revs or you risk having drained more out of the battery than you've put back! :lecturef_smilie:
Here's to Good Luck with charging your battery properly and then running it often enough/for long enough to keep it charged properly! :cheers: