What is that vent on back seat, right side?

It's pretty simple, at least on the 3rd gen. For 2nd gen, similar? On 3rd gen this is what I do:

1. Remove the fan inlet grill. It's part of the seatback, a thin wedge at the end, has a single bolt (requires 12 mm socket, and a 6" extension) at the bottom. You push down the seat pillow to reach the bolt. Once it's off the whole thing just lifts off of hooks. There's Velcro attachment at the bottom, you can disconnect completely, or leave it dangling. It helps to tilt the seat back forward a bit.

2. Remove the portion of the hatch floor attached to top of hybrid battery. This is largely attached with plastic clips that are just pried up to release. There's also one bolt, near the seat back. The plastic clips are VERY stubborn: the first time I removed it I thought something might break. Some popped off their (slotted) moorings on the hatch floor. I opted to remove them all, rely now on the bolt and a few hooks that are more than plenty to secure the floor.

3. You can now see the fan, at one end of the battery, plus plastic ducts between the rear seat intake grill and fan. It has a few push-in fasteners, with "Christmas tree" shaped fronds to grip. They can just be pried out, then the duct pulled off.

That's as much as you need to do, you clean the fan now, without removal. It's a "squirrel cage" style, with close spaced fins. Q-tips are good fit, between the fan blades. Also, run sort of duster wand through the duct work. Also vacuum what you can, then you compressed air, blow the dust out.


Viewed from the right side of back seat, looking down and slightly towards the passenger side:

Viewed from right side of back seat, looking towards rear:

Closer view, similar to above:

 

Excellent photos! Now I don't need to take that cooling system any further apart to satisfy my curiosity as to what it looks like!

 

Those pics were at a very recent cleaning, and really quite easy second time around. I've had a fairly tight filter behind the grill for most of its 50000+ kms, so maybe a factor. We've had a shiba enu in back, a fair number of times.

There was a layer of fine dust build up on fins of fan, and ducts were a bit dusty too. Not bad, but again, I'm sure the filter I installed helped.

I've swapped it for a more open mesh now, residential window big screen:

 

Is it too late to tell the OP that it's the air vent so the trunk monkey doesn't suffocate?

 

The vent in my (v)agon is under the rear passenger seat. My tendency to put boxes on the floor in front of the rear seat probably has to be modified. I think I'll put two strips of wood on the floor to make a tunnel to the vent.