This one is easy to explain, compared to the Native-rulership patterns, upon which it depends. It requires one-on-one rulership in that regard, and Apollo's Triangle, which I usually refer to as the Ascendant, and Gaia's Trident, or, the Age Indicator, become Native-rulers of Sagittarius, and of Taurus, respectively.
The process of transition, from one Sign to another, is what informs it. Each Sign is in a constant state of transition, which ends when it has become transformed into the next Sign, in Direct-motion. There are two other Signs involved in this process, a Primary, and a Secondary. The Primary, facilitates the transitional process from beginning to end, and its Native-ruler regulates the process. To determine the Facilitator and Regulator, start with the Modality of a Sign, then add the Element of the Sign into which it will eventually transform. So, Aquarius, is of Fixed-mode, and the transformation will be into Pisces, a Water-sign. Scorpio, which is the Fixed Water- sign, is the Facilitator, and it's Native-ruler, the Planet known as Pluto, is the Regulator.
Next, add the Element of the Sign, in this case, Air, to the Modality of, in this case, Pisces. That's Gemini, Mutable Air-sign, which is therefore in the role of Catalyst, for the transition. Mercury is Native-ruler of Gemini, and is the Motivator. The Secondary, Sign/Rulership pairing is "in service" to the Primary; in this case, that's Gemini/Mercury in service to Scorpio/Pluto. For an example, Mercury conducted the Souls of the Dead to the Underworld, as a service to Pluto. Pluto is in Gemini's Rulership group, in a voluntary Service-arrangement. And, Mercury is Beneficial-ruler for Scorpio.
The Regulator determines the nature and rate of the transitional process, with the cooperation of the Motivator. Gemini is the Catalytic-sign for Aquarius, and Scorpio is Companion-Sign.
That's the pattern for the rulership groupings. For Aquarius: Native-ruler, Ouranos; Regulating-ruler, Pluto; Motivational-ruler, Mercury; and, Service-ruler, the Moon (from Libra transitioning into Scorpio). Also, Aquarius is the Facilitator for Taurus, and the Motivator in that case, Jupiter, is therefore the Beneficial-ruler for Aquarius.
Also, I forgot to include Horus, as the Egyptian version of Apollo. The kind of Pharoah I mean is the early conception: The Savior and Good Shepherd, who made it possible for all Egyptians, including the "commoners", to enter the Heavens in the Afterlife by interceding on their behalf with Osiris (now known as Pluto), Judge of Souls.