Absence of mind; apparent thought, but real vacuity. The corresponding French expression explains it—sombre réverie. Sombre and brun both mean sad, melancholy, gloomy, dull.
Invention flags, his brain grows muddy, And black despair succeeds brown study.
Congreve: An Impossible Thing.
Anne Boleyn had a whole host of Browns, or “country cousins,” who were welcomed at Court in the reign of Elizabeth. The queen, however, was quick to see what was gauche, and did not scruple to reprove the Browns if she noticed anything in their conduct not comme il faut. Her bluntness of speech often “astonished the Browns.”
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894