I spent quite a bit of time looking into this, and I have hundreds of examples.
Here's what I've figured out so far...
In certain regions, the poofy beret was used in manuscripts to represent "the learned man". In other words, it represented a person of a certain status, who had knowledge (and was often passing this knowledge or general advice to a lower-status character in the image). In other words, it was not specific to the person's profession, but rather it denoted their status in the sense of being in a position to dispense advice.
In other areas, it represented a doctor (e.g., in earlier manuscripts and sometimes more southern manuscripts).
So, I think the time period and the region do matter in terms of interpreting the hat.
Another example... in France and the western HRE, the baggy sleeves often represented "our hero"—the central figure in the story (especially in romances). But, I discovered that in certain regions, and in earlier manuscripts, the baggy sleeves were sometimes reserved for the villain. For example, in the 14th century in some areas, Judas would be depicted with baggy sleeves. In other areas, and in 15th century manuscripts, more often the lover, the traveler, or the learner would have the baggy sleeves.
Here's what I've figured out so far...
In certain regions, the poofy beret was used in manuscripts to represent "the learned man". In other words, it represented a person of a certain status, who had knowledge (and was often passing this knowledge or general advice to a lower-status character in the image). In other words, it was not specific to the person's profession, but rather it denoted their status in the sense of being in a position to dispense advice.
In other areas, it represented a doctor (e.g., in earlier manuscripts and sometimes more southern manuscripts).
So, I think the time period and the region do matter in terms of interpreting the hat.
Another example... in France and the western HRE, the baggy sleeves often represented "our hero"—the central figure in the story (especially in romances). But, I discovered that in certain regions, and in earlier manuscripts, the baggy sleeves were sometimes reserved for the villain. For example, in the 14th century in some areas, Judas would be depicted with baggy sleeves. In other areas, and in 15th century manuscripts, more often the lover, the traveler, or the learner would have the baggy sleeves.