06 600ho switchback no lights at idle

Have you completely disconnected the battery? I'm not sure what a completely shorted battery would do because you do have a regulator/rectifier on that model with electric start. If that doesn't help I would suspect a corrosion problem on a connector in the lighting circuit. Unplug all connectors you can see and reconnect them to see if that helps. Also unplug the wire to tail light which goes under the seat. It tends to chafe through and shorts out to ground. If you have a voltmeter the lighting circuit (yellow wires) is AC voltage. Wiring diagram attached for a 2005. Yours should be the same.

I have a similar problem with my 2010 800 assault except I do not have an E-Start or battery. I rode it one day and worked perfect, the next morning I started it up and the lights and screen didn't turn on until it warmed up and still the screen/lights would intermittently turn off and reboot. It idles just fine and I checked the stator and replaced the VR, but it still didn't fix the problem.