I can't tell what charger that is. You say 15A on two leads. Is that a pos and a neg for one battery or is it a two battery(dual bank) charger? That would be two positive leads and one or two negative wires.
If the former, you may be charging only one battery.How many batteries in total and how many battery switches?
You didn't say how long the ignition was left on but in general it would have pulled several amps since the ECU at a minimum is drawing power as well as gauges, fuel pump at least for a short while and possible other parts of the motor.
If the charger is a 'smart' type, there should be different lights to or light patterns to tell you what it is doing, high charge, slow charge or maintain charge.
Was the charger off when you got that 11.5 volt reading?. It should be a lot higher if indeed the charger is powered on and working.
Make sure the charger is running, leave it for a few hours, turn it off and then read the battery voltage again. It should have increased. If it did continue charging until the battery reads about 12.5 volts (with the charger off)
If the standing battery voltage doesn't increase, you have a bad charger or it is not wired to that battery.
If you can start the motors on the good battery, start them and then switch to the bad battery ( passing through BOTH and never passed OFF with the motors running). If the motors continue to run, go for a ride and give the battery some time at speed. Hopefully it is OK and will take a charge.