The type of car is an inseparable semantic unit, while the type of a car consists of two parts with the first functioning as a property of the second, so we can change the type to the color or some other feature.
I'm not completely sure but I
think you're on the right lines. Let me present this in a different way.
You can use certain 'category' words (that's my made-up term) in two quite distinct senses—as
general abstract concepts and as a
discrete labels of description. Let's take
colour as an example.
The colour of car you drive says a lot about you.
In the sentence above,
colour of car essentially means red or blue or black or yellow or pink. That is to say, the word
colour has the sense of referring to a very particular wavelength of light. This is the sense we use when we say that 'green
is a colour'. We're talking about one discrete thing among many. The speaker is thinking that there's a finite number of different colours available. Cars come in certain colours.
The colour of a T-shirt fades after several washes.
Here, the word
colour refers to the idea of colour, as an abstract concept. It's an open, non-discrete class. That's why it can be followed by an indefinite noun phrase. We're not talking about the particular colour (pink or green) of the T-shirt, but about the general quality of colour itself.
If this difference isn't clear, let's try another category word: size. Similarly, size can refer to a very general abstract concept of extension in space, but it can also refer to one of a group of particular instantiations of the general concept—for example, small/medium/large.
The size of a man's hands can tell you a lot about him. [open class]
How much you spend in McDonald's depends on the size of drink you order. [discrete class]
Do you see? When you use a zero article, you're thinking about a discrete class, as opposed to an open one. It's the same with 'type', and other 'category' words.
Considering type as a separable feature, and as long as The colour of the car he drives can tell you a lot about him is correct, would this be correct:
The type of the car he drives can tell you a lot about him.
So in both those examples, you ought to use the zero article, because (I think) you're thinking about discrete classes. That is, you're thinking that cars come in certain discrete colours and types, and you can match these particular colours and types with particular character types.
(I live in hope that one day you might ask an
easy question. Is that possible?)