hey all,
An update to this topic if anyone needs it...
Eventually, I found the unit, but was installed in the drivers footwell, and on top of that, it's different to what's shown in the manual, but it's still a Genuine Toyota accessory.
part number is: PZQ71-12071, and it looks like it might be the single button remote, which is also an alarm.
I'll post more when I know more.