Do you have dummy lights on the panel, for temp, oil pressure and charging?
It may be the charging - at low rpms, maybe there is a problem that the alternator is not charging. Easy to check. Test any 12v connection point, when the motor is reving highre, and make sure you are showing something like 13 volts +. Then lower rpms until the alarm sound and meter again. If you are only showing less than 13 volts, you are not charging.
At that point, you could troubleshoot alternator belt tension, or take off the alternator and take it t ohave tested.