Isaiah 11:2 may yield some clues about the reference. To say that the prophet delineates seven spirits of God is way more than a stretch, but it certainly suggests something. It seems the one Spirit can be properly referred to by his various attributes. The apocalyptic designation would perhaps be better understood, in that light, as the sevenfold Spirit of God, understanding the seven as an idealized expression of perfection in every aspect of God, the Spirit's being. There are other spirits about beside God, but by this reckoning, none of them could be called sevenfold.
That is generally verified by John's introduction of the the sevenfold Spirit in conjunction with the unnamed God on the throne (the Father) and Jesus Christ, the firstborn from the dead. The sevenfold Spirit is therefore part of a trinitarian formulation identifying the God who is controlling all that is about to be unfolded prophetically. As the Father and Son are perfect and united in purpose, so too with them is the oft forgotten member of the trinity, the Holy Spirit, united in purpose and perfect as well.
Between John's introduction and latter apocalyptic references to the seven Spirits of God, the attributes that seem most in focus for the Apostle (as opposed to those Isaiah highlighted) are omniscience and omnipresence. God on the throne is timeless (he was, and is, and is to come) and his sevenfold Spirit before him is likewise always present in the always present. The light of his perfection (lamps) always emanates from the throne room of God to the farthest places, illuminating the deepest darkness of space, time and spirit, bringing all within clear sight (eyes) of the God who sees all.