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This is a question about the real world.

In the story that I am writing, one person suffers the destruction of (most of) their brainstem and cerebellum. Other parts of the brain and body remain largely unaffected or receive only minor injuries that can be healed (e.g. a fracture of a bone). The face remains completely unscathed, maybe with the exception of the lower jaw.

I have attempted to research head injuries in traffic incidents, but have only been able to find statistics or generalities, and all examples of head injuries that I found are described as involving either the whole brain (e.g. concussion) or other parts of the head (e.g. injuries to the face when wearing a helmet).

What I probably need is some kind of Phineas Gage accident, where not the whole head is bashed against another vehicle or the ground, but where a slim, sharp object like a spiked fence post or torn vehicle door does some very limited damage.

Ideally the victim of the accident was riding a bike and the perpetrator was driving a car. If the victim is not riding a bike, they need to be travelling individually (e.g. in a car or on foot), not in public transportation (bus or train).

The victim dies from the injury.

Note.

The cause of the injury must be a traffic accident (not a bomb damaging cars passing by or a terrorist knifing passengers).

You've basically answered your own question already (as per my comment: handwave a "one in a million" accident involving a suitably sized sharp object and don't go into too many details).

For a specific example of a pathology which can damage the brainstem, consider coning (content warning: contains a picture of a preseved dead infant) or "tonsillar cerebral herniation", where an increase in intracranial pressure basically forces your brain out through the foramen magnum (a great example of everything sounding more serious and sciency when said in latin; "big hole" doesn't make you sound nearly as knowledgeable) brainstem first. The crushing and malformation of the brainstem results in death due to respiratory arrest. Damage to the cerebellum may also arise, but as this will generally occur after serious damage to the brainstem it isn't usually relevant, though it may well be useful for your needs.

A rise in ICP is generally caused by either cerebral haemorrhage or cerebral oedema. The former would have to be quite localised at the base of the skull, if you wanted the rest of the brain to remain more or less intact, I think... haemorrhages elsewhere do risk compressing other bits of the brain, though of course the inability to breath caused by brainstem damage will irreversably damage all those cells anyway without very prompt (and potentially science-fictional) intervention. It isn't obvious that in traumatic brain injury cerebral oedema could occur without cerebral haemorrhage, but I Am Not A Doctor (and even then, you may need to ask a neurologist or ER specialist rather than just any medic).

So there you have it... solid bang on the base of the skull (but other bits of the head can work just as well), doesn't even need to be hard enough to fracture (though it might help). Victim is likely to be knocked out immediately and fail to recover consciousness before death. Surprisingly, it is possible to sustain a fatal head injury but be entirely capable of getting up and tottering around for a bit before increased ICP crushed your brainstem and down you go. Mortality figures are high, so even with prompt specialist medical care there's a good chance they won't survive.

Riding a bike without a helmet and being knocked off or even just crashing all by yourself seems like a good way to have this happen to you. Collision speeds don't need to be too high, so long as there is something suitably hard and ideally edged (like a curb, or the top of a wall) to concentrate forces in the right place.

During car crashes not everything stops at once. This is why you are warned never to place anything loose on either the dashboard or the space behind the chairs at a height. If you crash into a car at 50km/h and a smartphone is behind you at neck height it'll hit you with 50km/h. That is going to deal a lot of damage if not kill you. Even without a crash but when emergency breaking this can be lethal if you go faat enough.

Now imagine you having something larger, maybe you were transporting a pole, a shovel, a few bricks for a wall you were going to build, maybe your groceries had a literpack sticking out the top that smashes the back of your neck and head after a sudden stop. Hit he back of your head hard enough and it can damage the brainstem and cerebellum along with the back of the skull enough for death to occur.