....inverter still draws the batteries down even if the inverter switch is turned off.
On my 2007 with Tripp-Lite inverter. It could be the same on your 2009. There are 3 ways to turn off your inverter. Two methods kill the inveter completely, one partially.
1) The main kill switch by the entry door - Turning this switch off kills 100% of the RV 12v system including the inverter. There is no power drain. No lights or anything else will function. This switch should never be used when camping because it also kills the fridge regardless of which mode it is opperating under. Use that kill switch and your food will spoil.
2) The switch physically located on the inverter itself - Turning this switch off, kills the inverter 100%, but keeps 12v opperations functioning as normal. All lights, exhaust fans, etc still work. I use this switch when leaving the motor home for the day. There is NO power draw from the inverter this way. Unfortunately the switch is not convenient to get to.
3) The Tripp-Lite control panel switch mounted under the fridge - In my opinion, this switch is pretty much useless. With the phone jack plugged into it's backside, the inverter always draws 12-amps sitting idle which is rediculous. It's only benefit is to always have 110v available which is fine for people who hop from one RV park to another. But for primitive campers like me, this is NOT good. With the phone jack unplugged and inverter turned off using the Tripp-Lite control panel, it still draws 1-amp just sitting idle. I want zero draw so I turn on the inverter using the switch on the inverter, only under the following conditions. 1) when I need 110v 2) when plugged into shore power to charge the batteries 3) when generator is running to charge the batteries.
I think PC-USA switched to the later inverter to eliminate this saga.