The uncle is not a category classical astrology treats on its own account. He arrives through a technique rather than a doctrine, and the technique is derived houses, often called turning the chart.
The method is arithmetic. Any house may be treated as the first house of the person it signifies, and the other eleven counted round from it. If the fourth house is the father, then the father's own second house of money is the fifth of the radical chart, his third house of brothers and sisters is the sixth, and his seventh house of marriage is the tenth. The father's brother, being a sibling of the person the fourth signifies, lands in the sixth.
Lilly reaches the same answer from the other direction. His catalogue of the sixth house lists servants, sickness, small cattle, and uncles and aunts on the father's side, without deriving any of it. The derivation and the catalogue agree, which is the best evidence readily available that the turning method was already doing this work when the catalogue was written down, rather than being applied to it afterwards.
Run the same arithmetic from the tenth, where Lilly puts the mother, and the mother's brother falls in the twelfth. The two uncles are therefore not one thing in the chart. They occupy houses of different character, the sixth of service and illness and the twelfth of confinement and what is hidden, and a reading that treats an uncle generically has thrown away the distinction the method exists to make.