Running in neutral requires the neutral switch on the gearbox to activate the middle relay.
No neutral indicator light suggests a bad connection to the switch ( easy, just behind the starter , clean it, crimp carefully, pack with dielectric grease) or a bad neutral switch ( easy , again it may be removed and cleaned, worst case - replaced).
Certainly the middle relay is suspect if the neutral indicator lights but the bike still won't run with the side stand down. Good news there is that the sidestand switch works.
Remember the 'sidestand safety relay' is activated by the neutral switch.