If the reason is actually to cool the brain I would suggest, whilst only having my own experience to draw from, that an ice pack on the head would be less effective than cooling the blood supply that actually enters the brain. An ice pack on the head would seem to mainly cool the skin, as the skin, muscles, skull and a significant amount of fluid is between the brain and the top of the head. Without being a medical type person I have no idea if the blood on the outside of skull actually enters the brain, it would seem poor 'design' if it did directly in significant quantities, as a small cut on the head could, in that case, empty the brain
An ice pack on the neck over the main blood vessels entering the brain would have the possibility of cooling the blood entering the brain, a bit, so would be my prefered option if trying to cool down the brain.
I should point out that whilst I used ice on my neck it was not over these blood vessels, it was over the base of the skull and the portion of the neck adjacent - where the spine hits the skull and a few inches down, as this is the area that was overheating/hot. The effect was short lived (i.e. if the ice was taken away/melted then within a few minutes I would need it back).
It was never my intention, or aim, to cool the blood to my brain, it was my intention to cool down a hot bit, as doing so made me feel better, but I suspect if cooling the brain was your aim, it would be a better approach.
I have absolutely no idea what good putting an ice pack on someone's head is supposed to do re; cooling the brain, and it hurts, but if it works for you then carry on.
ETA - having given it a few minutes further thought it occurs that an ice pack on the head would, if continued long enough, cool the blood, just not brain specific. This is why people used to wear hats in a cold environment, a lot of body heat can be lost through the head if it's cold enough, but I would question if this could significantly affect brain temperature until the heat loss was serious (i.e. the blood would need to be cool enough to affect other organs, the brain may be, after all, a 'protected' organ, possibly capable of generating significant amounts of heat independently, at least so the number of calories it can burn would suggest.