I did a little searching on the web. It appears that the part number for the connector itself might be 90980-12C39. Referred to as 12C39. This looks to be a Toyota number possibly. This site looks to show it but is not in English.
Another option to look at is the Toyota Online parts this is a possible place, but I cannot fully confirm it either.
This might be a start for you at least. It appears there are harnesses out there for what you would like to do.
I am sorry, but it looks like we will not have that exact connector.
