It is easy to identify Rousseau's ideology in Faust Part I, but harder to find a trace of it in Part II. The reasons are three-fold. First, sixty years past between the originally published fragments and Goethe's writing of Part II, recommencing it after his friends and admirers begged him to complete Faust before the end of his life. Ultimately, Goethe died just days after completing Faust Parts I and II. It was sealed, not be opened until after his death.
Second, Faust was begun in 1772 and helped launch the Romantic period. In 1777, because of a young woman's self-inflicted death influenced by The Sorrows of Young Werther, a copy of which was in her pocket, Goethe renounced all association with Rousseau-influenced Romanticism.
Third, Goethe completed Faust in the style of Classical drama, with no Romanticism in Faust Part II, which is steeped instead in the classicalist’s search for knowledge and reason as is proven by settings, characters, themes, and allusions. Yet, there are three places where Rousseau-type feeling might be interpreted as representing Rousseau's man of feeling.
The first is Faust's encounter with Helen of Troy whom Mephistopheles (Mephisto) has liberated from the classical underworld. It's interesting to note that when they meet in Part II, Helen is speaking in Homeric verse and Faust, speaking in Elizabethan verse, teaches her rhyming.
But teach me why that man spoke aloud
With curious speech, familiar but strange.
Faust loves Helen, who was the first one to stir his passion--before Mephisto coerced him into taking the youth and love potion that led to Gretchen's undoing. Their courtship and life together is built on Rousseau's idea of the man of feeling--one who doesn't interrupt his flow of feeling with the rational task of selecting, combining, and choosing language to produce an affect of wit and the persuasive power of passion.
The second is the son that Faust and Helen have. Euphorion is precocious, possessing a spirit of adventure and exploration. Helen and Faust deeply love and pamper their son: "It requires two noble hearts / For Love to bless humanity." One day, Euphorion insists that he can fly and falls to his death: "Onward! I must! I must! / Let me but fly!" The feeling Faust displays can link him to Rousseau's man of feeling. It is heightened by his sorrow when Helen is called back to the underworld when their son is no more: "Mother, don't leave me alone / In the shadows' domain!"
The third is at the end of Faust's life. He has completed almost all parts of his land reclamation project yet is plagued because one old peasant couple has held out against his entreaties and clings to their land, trees, and chapel--the chapel gives Faust a dread feeling. Mephisto goes too far when Faust in haste requires that the couple be moved by force to another plot of land that he has selected. The old couple dies of terror together when Mephisto and his generals storm in. After Faust's feeling of rage at Mephisto is spent, his feelings turn to remorse and he says, "Quickly said, too quickly done, I fear!" His final moments are spent in exalted feelings--further connecting him to the man of felling--after being blinded by Care, as he envisions a new achievement that will house millions:
My last and greatest act of will
Succeeds when ...
[I] make room for many a million.