What kind of person would a shallow-pate be?
If someone calls you a shallow-pate, it's not a compliment! A pate is the head, brain, or intellect. Combine that with shallow, and you may be able to guess what it means: a person who lacks depth or intelligence.
In The Awakening, Edna Pontellier hosts an elegant dinner party for select guests:
There were Mr. and Mrs. Merriman, a pretty vivacious little woman in the thirties; her husband, a jovial fellow, something of a shallow-pate, who laughed a good deal at other people's witticisms, and had thereby made himself extremely popular.