He doesn't testify about Himself.
John 16:13-14 KJV
13) Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
14) He shall glorify me: for he shall receive of mine, and shall shew it unto you.
Much love!
The spirit you speak of is the gift of the holy spirit that came on the day of Pentecost. See Acts chapter 2. It's the Christ in us and has nothing to do with a god person.