Well, there may be a chance I am wrong, because I am not Japanese =).
Doing a quick search, there is a fun fact about China usage of “red car” that is interesting that I thought you may want to know.
In Romance of the Three Kingdoms, there is a “red hare” horse. 赤兔马 It belong to the super general Lu Bu, given to him by Cao Cao.
There are some Chinese guy who makes number plates like this:
Which literally translate to “red hare famous car”. So who knows, maybe the 赤 is not actually a Japanese thing but a Chinese which will then stand for “This car is fast!”