IMHO and from personal experience the headstock size (maybe not so much the shape) does impart a small bit of tone shaping to the bass.Even true of my '64 Embassy, hence the Rotos on it. Same electronics and wood. Could it be that tone is really in the shape?
From a physics standpoint any significant change to the neck of a bass can impact the natural frequency of that bass. It may move a dead spot from one fret to the next or lessen dead spots or woof tones or increase or reduce the attack or decay of certain fretted notes.I haven't messed with it enough to know how to predict what neck change will make what difference but I have experienced it first hand on a number of my builds.
The headstock size seems to be one of the bigger factors in how the bass reacts to the strings, along with wood type and nut material. I'm sure there are many that will disagree with my observations, they are subtle so they can easily go unnoticed in a mix or not heard by those that aren't listening with a critical ear. YMMV


