Since edits must be accomplished within 10 minutes, here's how I intended to edit:
Just installed this in my Toyota Yaris 2019. Yes it fits. Toyota was hesitant to sell it to me because they weren't sure it was for this car, but it fits perfectly.
The "mystery plastic pieces".... You could go without them, but I believe they're intended to make it pivot more smoothly and to reduce wear. They go between the pivoting portion and the tower "fork". Notice the disks fit right in the holes and can swivel in that position. Place the disks in their holes, then using scotch tape or painter's tape (something not very sticky) I held the plastic pieces and the disks in place with a portion of tape exposed outside the "fork", before placing the armrest between them on the tower. To get them properly aligned in advance, I ran the bolt through without the armrest. Once the amrest was in place bolt was placed through all parts, I pulled the tape out.
Also, the end caps fit just fine, but you have to get them in right. One is for the left and the other is for the right -- They're not identical. There's a letter P stamped inside one and a letter D on the other. (Ah, I just realized that means Driver and Passenger.) There is a small notch in each with a corresponding tab for the side they go on. In both cases this notch is diagonally down and toward the front of the car.