I think that the only practical way to test the inverter is to install it and see if the car works or not.
I couldn't agree more. To diagnose would require taking it apart, and for what purpose? Much better just to plug her in, and see what happens, trust me, you will know if it works or not MUCH faster, than any sort of external testing!
I am not aware of any available equipment or procedures to do this (inside or outside the Toyota dynasty). I suspect a sharp EE with a lot of time and interest could develop some procedures that would allow you to identify some failures on the bench assuming you had the right equipment, but to develop a full test platform would be prohibitively expensive. I think you are stuck with 'functional test' in the car. I would be acutely interested in any bench testing that has been developed. Eric PS: An interesting thread would be: After you put it in the car, what can you look at to make sure its good? Techstream exposes a lot of information.