If you want to get anal (and who doesn’t?), the seal he uses is the seal of Lucifer as Ruler of Asia (which may mean The East or Air?), as opposed to his Seal which looks like it’s meant to be used as a talismanic gateway. Also worth noting, like almost all the demonic seals floating around out there, it’s the Mathers rendering as published by Waite, and Mathers deliberately altered nearly all of the talismans and seals he published, though only slightly, but it’s a difference a sensitive person can really notice. For example, the Lucifer/Asia seal that most people see is elongated into a distorted V or funnel, while the original manuscripts show more of a pyramid looking design. Compare between the Peterson editions of the Grimorium Verum and Lesser Key and Waite’s Book of Ceremonial Magic, see if you don’t feel the difference. The seals in Peterson’s Lesser Key have that “alive” feeling like Enochian tables.
ANYWAY… I have an idea about this whole changing Watchtowers thing, and it’s only my idea… But remember that in old school Planetary Magic, you rig up magic squares using astrological combinations, then perform certain mathematical operations on those squares to get the names of the angels and demons and whatnot that specialize in what you need. You look at the job you need done and put together the planets/signs that seem to best produce this.
Now in the Goetia, the spirits are mapped astrologically, each having a planet and zodiacal sign. So it seems to me that the right combination of the right four Chiefs or Kings…and remember the Kings are associated with the Sun and the Sun is always the Key… different alignments should produce different initiations with different emphases… it seems to me that the systems which emphasize Lucifer, Satan, Satanachia, Lucifuge Rofocale are about total power, total ascent, total right, with an emphasis on the right to absolute rulership over one’s own universe, even unto subjugation, domination, and severe violations of order. It’s the Initiation into the Right of Absolute Rulership.
Initiations that Emphasize Paimon, Azazel, Ashtoreth, Asmoday, Belial, these are architectural initiations - the establishment of empire. There are probably more of them… I’ve been explicitly told multiple times by Lucifer and others that they have thousands of initiatory pathways, and maybe this is a part of that.