The date is 25/09/2017 09:36

'16 Toyo Avalon Limited doesn't have a docking hole; fob just needs to
be in/near the car.

Two things are required.
1. The key
2. The immobilizer

There is a third doohickey which is just a remote unlock/lock thingey.
Pictures are in the original post.
http://www.bild.me/bild.php?file=4828475keyfob.jpg

The key is a duplicate without a chip (it's all metal).
The plastic key on the second fob also has no chip (Home Depot tested it).

So you need two things to start the car.
1. the key
2. the immobilizer

But none of that has anything to do with the fact that the car locks all
the doors when it moves forward and when it sits for a while.

I only wish it could be turned off as my friend said she hates that
'feature' of the Toyota Camry 2005.