I do find the Bible supporting the idea of the Trinity but in quite indirect ways. It starts with creation with references to the Spirit hovering over the chaos, but when Elohim says "let us make humankind in our image..." that suggests some form of duality. Then there are in the OT numerous references to the Son of Man, etc. But, the actual doctrine is certainly an extrapolation and I am sure much depends on John 1 (The Word became flesh and lived among us..).
Reading both Thomas Aquinas and Hannah Arendt discussing the mind has helped me address this and derive my own understanding using our minds as examples. We have thoughts, we have language or expressions, and we have intention put into action, Thought, Word and Deed--all aspects of a single mind.