I think you understand this part, but I'm going to state it anyway because it sets up the harder part you're asking about:
When a rigger jumps in, the vehicle's matrix icon merges with the rigger's persona. Two icons become one, and the one is a continuation of the rigger's persona rather than a gestalt of the two.
On to the harder part:
If you're looking at a car's matrix icon, and then some rigger jumps in, what do you see happening?
The first wrinkle is that it's unspecified as to whether "merging" means as far as the matrix is concerned there's two physical locations still, or just the one. 9 times out of 10 it doesn't matter because you can't DO anything to the car in the matrix whilst a rigger is jumped in*... but this scenario would be one of those 10s. So, it matters whether distance-based Noise is measured from the observer to the car or from the observer to the rigger. I would say that because the car's matrix icon is merged into the rigger's, the distance to the car itself ceases to be relevant and therefore distance is a question of observer to the rigger.
And with that being the case, if the rigger is not within 100m of the observer, spotting is not automatic. A Matrix Perception test would now be called for. Likewise, if the car was not running silent and then a silent-running rigger jumped in, a Matrix Perception test would also be necessary.
If the matrix perception test is successful (or wasn't necessary in the first place, i.e. the rigger is within 100m of the observer and not running silent): The observer would see the car's icon merge with the rigger's persona. The exact details are irrelevant, and based on iconography anyway. Is the rigger a neo-cowboy? Maybe the car's icon momentarily transforms into a horse during the merging process while the rigger's cowboy icon changes into a cowboy riding a horse. Or, maybe the car's icon melts into a million motes of light and reform as the rigger's icon. Infinite possibilities, but they're all rules-indistinguishable.
If the matrix perception test is unsuccessful: Essentially, the car's matrix icon just disappears. Maybe the GM might throw a bone by saying perhaps the Cowboy rigger's car turned into horse, then galloped off into the unknown. Maybe the car dissolved into a million motes of light, then they all faded out. Again, rules-wise, this is all roleplaying fluff. Rules-wise, what's important is the observer no longer has the car's matrix icon spotted.
*EDIT: This is a tangent, and it might be something you already grok, but I'm gonna throw it out there anyway because it's a very interesting way the matrix rules work: Once a rigger is jumped in to a car, you cannot trace the physical location of that car. It has no matrix icon! All you can target with a trace icon matrix action is the rigger's persona, which may or may not be inside that car... If you want to trace the CAR once a rigger jumps in, you need to affix some sort of tracking signal! Tracer bullets, RFID tags, etc. That, or wait for the rigger to cease jumping in so the car's matrix icon re-emerges...