I'm not convinced the rear cool box is a great design. Given that it only has one vent to the rear a/c system, there can be no flow of cold air through it. (And also noting that it's not a refrigerator per-se.)
Even with the rear a/c set to max, any object placed in the cool box doesn't really seem to get cool. (But to be sure I'll try it with a bottle of water, starting at ambient temperature.)
(Yes the vent flap is open!)
Not sure how many US cars had this feature, seems to be a ski-hatch generally.

 

Mine has the CoolBox and when the air-con was working it could cool a can of soda down to about 5C/40F in a about an hour.
It runs off of the rear AC circuit so check if the rear AC vents are putting out cold air as the rear AC refrigerant lines are a common fault and often end up being capped off as the front AC is adequate to cool the whole car under most circumstances.
If the rear AC is working well, then it should cool your soda can down pretty quickly.
Plastic bottles will take longer as the plastic is an efficient insulator.

 

If you try to put a room temperature soda in the box and expect it to be cool, that probably won't meet your expectation. However, if you have something already cold, ithen the cooler make more sense. I don't use it often since most of the time just me driving back and forth to work. My son uses it once a while they he's in the back, no compliant

 

So the cool box only works if you turn on rear AC and not the front?

 

Coolbox operates only when rear AC is on. There is a shutter flap at the top of the coolbox, make sure it's open, otherwise no cold air gets blown in.

Protip: the coolbox fits six 330/355mL beer/soda cans PLUS 3 WhiteClaw/RedBull cans on top. The trick is to remove the top row middle 330/355 can, slide the 3 skinny cans across the top of the stack, then put the sixth 330/355 can in.

For best cooling, set rear AC ON and fan speed to HIGH (requires tapping the Manual button a few times). This will chill the nine cans from warm to ice cold in under an hour.

 

I love my coolbox!! Can chill drinks or other items for long drives or just around town. I use it for carting around my home made ice cream on shorter trips! Soda cans or bottled water stay ice cold. Can even cool them down from room temp in about an hour or so. Back when I took clients around they LOVED this feature!!

 

Update:

It does indeed seem that my rear evaporator has been isolated and the pipes capped off. Only warm air comes out of the vents over the rear doors and likewise into the cool box. (Luckily the ones on the back of the front arm rest/console do blow out reasonably cold air.)

More than a year on I'm still struggling to bond with this car. In some ways it's a revelation; in others, against the backdrop of a 1998 LS400, it's a huge disappointment.

 

How is the 98 LS400 better? I’ve heard a few things but curious as to your take.

 

Ride, styling, road-presence, reliability of on-board equipment generally.

 

I also have the '98 LS400, I would add - simplicity of the design, ergonomics, visibility, and quality of the leather. And, the '98 gets noticeably better fuel economy than my '05 LS430. The LS400 does have a significantly smaller trunk however. I would say that the ride is slightly better in the LS430, at least in my experience.

 

interesting thx. What size wheels on both cars?

I’m wondering if the ride difference just comes down to sidewall height or if it’s a suspension design difference.

I’ve got an 04 UL and the ride is ok to good but not amazing on air suspension with 17’s at factory psi of 32. I replaced the two front air struts a few years ago and that helped a lot. Wondering if it may be time for the rears too, but they still hold air and are not leaking. Maybe some other suspension parts can be changed out first at less expense?

Ya I agree the UL leather is just ok, not great. I think my older Lexus cars had better leather, my two SC400’s especially.

 

My '98 rides on 16 inch wheels, came with brand new Toyo Eclipse tires. My '05 rides on 18 inch wheel, with Pirelli P Zero All Season Plus tires. (Excellent, by the way, very quiet and lasting a long time). The '98 has a much taller sidewall and I am sure it makes a difference on the ride.