While the Tarot has been associated with many spirits and spiritual systems, they have not been as accessible to the user. With Crystals and my book The Tarot and the Magus, this situation is changing.
The spirits of Liber 231 are the prime rulers of the 22 Major cards, rather than the Kabbalistic attributions of the 22 letters of the Hebrew alphabet. See the Powers of Liber 231
The 16 Court Cards are associated with the Tablet of Union, which unifies the four elements and spirit in the Enochian Magical system. The unification of the four elements results in Akasha, the field from which manifestation takes place.
The 36 Minor cards are associated with Goetic Spirits. My own experience tells me that the Goetic connection with the 36 decanates is somewhat tenuous, but the spirits themselves are not particularly bothered about it. Meditation on the minor card associated with the Goetic Spirit (particularly if it is an unaspected card in the Opening of the Key Spread).