Assuming the switch is in the USE position rather than STORE, the indicator is showing the presence of 12v power. When the light goes out, power has (supposedly) gone away. ON the surface it seems that you are losing power and then having it come back on, so my first step would be to check with a voltmeter to verify system voltage as the light goes through its cycle. If the voltmeter agrees that 12v battery power is coming and going, you would seem to have a charger or battery issue. If the voltmeter shows that 12v power remains stable, then the problem is the electronics in the disconnect unit.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL