In regards to Millennium Jade. This was an exclusive colour for the '02 R34 V-spec II Nür in the same was that Silica Breath was exclusive to the luxury focused '01 M-spec. Unlike the latter which was brought back for the 45th Anniversary R35 GT-R Millennium Jade does not feature on any other Skyline or GT-R model.
For the LHD R35 I have my own theories...
In recent releases, Gran Turismo has tended to opt for US or European variants of certain models. Perhaps it's an effort to appeal to a larger global market since most countries drive on the wrong side of the car maybe they think people will feel more at home if the cars in games are left-handed too.
I've also wondered if the LHD choice was made with GT Sport's race car variants in mind too. As most modern racers are built LHD (supposedly it's better for seeing the apex*) it would make more sense to model the RHD road car to make converting to track spec easier.
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* [Off on a slight tangent] Whenever I've seen the subject brought up on TV coverage that's the excuse the drivers tend to use. I'm not sure I believe it TBH as surely that's only an improvement for right hand bends. In the old days when race cars were more production-based, being L/RHD was determined by either the country the car was built (Since most cars are just converted road cars you go with what's available) or where people had the luxury of manufacturer backing, what the car was originally designed to be. In the 90's BTCC for example, the BMW 318i's were built LHD as it meant all the components were in their optimal spot, whereas the rest of the field were built RHD as that’s what the base cars (mainly Japanese and British-built European) were designed to be.
Most road cars are designed as L/RHD then converted for certain markets. 99% of JDM cars are designed to be RHD therefore all the components (engine/gearbox placement, brake master cylinder, even handbrake position etc) are positioned in optimal places. For foreign markets things are swapped over or where this isn't possible funky linkages are required making the setup less than ideal (see the Peugeot 206's brake pedal arrangement in RHD cars that places a linkage going from one side to the other behind the dash).
Sometimes these can be big optimal factors such as 90's Honda Civics that have the engine on the right hand side of the bay, resulting in the weight offsetting that of the driver leading to better balance. In LHD applications the driver is sat on the same side as the engine meaning the weight isn't as evenly distributed. Common complaints in the aftermarket scene is that LHD Civics suspension tends to sag on the driver's side as a result.
In most VAG and BMW cars that I've been in, the foot well on RHD is cramped with the pedals all bunched up. As it's designed to be a primarily LHD car parts of gearbox are positioned to right-hand side resulting in the tunnel encroaching into the left side. The Volvo V40 was slated in reviews for not having a clutch rest (dead pedal) as there was no space due to the floor pan being so heavily LHD biased. By comparison most JDM cars have a bigger right-hand foot well as the gearboxes have all their 'sticky outy' bits to the left side.