I made a sketch of the relay location and socket pin numbers, and a list of where each is connected.
http://members.cox.net/n0v8or/Avalon backlite grid relay.jpg

All defroster components can be tested from these pins. You can check the relay itself, as well as the control software and body computer, by holding a finger om the relay while a helper turns on and off the defroster button. You should clearly feel the contacts close.

 

Thanks for the advice. Here in Northwestern New Mexico it can get below zero in the winter! Most of NM can get pretty cold in the winter -- even the Southern areas can get below freezing sometimes.

 

I'm surprised you ever use the rear window defroester in NM. It must get colder at night than I imagined. This same 50A fuse also protects the side mirror heaters (if your Avalon has them). If you could determine if they (the mirror heaters) are working, the fuse and relay could be eliminated as a cause, leaving a broken wire at the window grid termination as more likely.

If you have a volt-ohm meter and are comfortable using it, I can describe where to probe the relay socket (after pulling the relay) to determine if the fuse, wiring, and heater grid are OK.

 

Thanks! I found it, but it doesn't come out easily and I don't want to do it wrong. I like your idea of asking a tech.

 

There is some sort of 50A fuse under the long bars located toward the front and engine side of the fuse/relay box. Unfortunately, I have no idea how you change it or where to get one. I would take a box of donuts (a form of currency here in New England) to the local dealer and strike up a conversation with one of the techs out having a smoke. This tactic has always worked for me.

In my experience, these high-amperage fuses rarely ever blow. The relay is another possible point of failure. I would listen for a "click" while a helper operates the defroster switch (ignition on; engine off).