OP: How do Trinitarians - who hold the Holy Spirit is a co-equal person of the Godhead - understand this verse?
Since Christ references God the Spirit, but not God the Father, earlier in the discourse at Mark 13:11 as knowing what to say, it (the OP) is a non-starter of a question, unless one wants to say there is only one God the Spirit by cherry-picking verses out of context and ignoring the whole of Scripture.
But when they shall lead you, and deliver you up, take no thought beforehand what ye shall speak, neither do ye premeditate: but whatsoever shall be given you in that hour, that speak ye: for it is not ye that speak, but the Holy Ghost. Mark 13:11