I had to determine that with Olympia (the main character in Weight of a Flame, the Passion of Olympia Morata). Being historical fiction, I could not make it up. I had to study her letters.
Her perceived needs and wants were obvious. She wanted to use her talents. She wanted to please her father, and others in general. She wanted to find a husband who appreciated her skills.
Her hidden need was not as clear. I had to go to the end of her life to find it, tracing it back to the start.
I remember sitting on a train in Italy, travelling back from Ferrara, her hometown, reading her last letters. Suddenly I saw something I had never noticed before - a repeated, almost unexpected emphasis on God's strength. She talked about it in almost every letter, with insistence, as if she were trying to convey a newly found treasure.
When did it start? Soon after she arrived in Heidelberg, giving signs of a mortal and incurable illness. What had happened? Just before this, she was a guest at the house of the Counts of Erbach, and was struck by their devotion to God. She had especially befriendedf the countess, Elizabeth, who apparently had been plagued by many ailments ever since she got married. That's when all seemed to make sense - maybe, Elizabeth said something to encourage her to rely on God's strength.
Being a work of historical "fiction," I was free to follow my instincts as much as the actual documentation. I began to see Olympia's character arc right in her letters. She started out as a young, talented woman, eager to please others, fearful of their opinions, and not very convinced of her faith in God. She ended with a deep faith and a total reliance on God's strength. The end result was the fulfillment of her hidden need, even if she didn't know she had it.
I then made that yearning the motivating force of her life from the beginning - a yearning for God, a God she came to know slowly through her life, first as Truth, in a letter by her father (this is a bit of fiction - the letter is true and so is her realization, but I put them together to give it a context); then as Truth worth dying for, in the prison with Fanini; then as Comfort, in her travels to Germany and throughout the war; as Fulfillment, in her meeting with the Fuggers (another bit of fiction - the meeting happened and the lesson was learned, but maybe not simultaneously); and finally as Strength.
Writing historical fiction is interesting, because even when we recognize a character arc, our hero or heroine doesn't usually follow it in a systematic manner. There are ups and downs, few steps forward and some back. Even after finding true faith in God, Olympia kept harboring a resentment for the people who had offended her, until the very end, which is what makes the story much better than a prefabricated account that goes from weak to strong, unbelieving to believing, bad to good.