The Lord Jesus has a complete human nature, which includes having a human will.
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St. Thomas uses the term “accidental” in a technical sense different from what we are used to. He does not mean inadvertent. By “accidental” he means not pertaining to the essence. An apple could be red or green; either one is essentially an apple. The color is an “accidental” quality.
Also, remember how we tackled the terms supposit and hypostasis. This has proved over and over again to be a stumbling block for faith in the Incarnation: God Personally took our human nature to Himself. Jesus Christ is a divine Person, the Almighty Creator and Lord of all, Who Personally is a man, a human being, like us in every way except sin.
Christ’s soul and body are united, just like our souls are united to our bodies. Christ’s human nature subsists in His divine Person.
He in one individual.
The Church has formulated Her doctrine on the Incarnation in order to harmonize with the way Sacred Scripture ascribes both divine and human things to the one Person, Jesus Christ. (The communication of idioms.)
Father Mark White Blog 