If the Son does whatever the Father does (John 5:19), does that mean the Father also incarnated for the Son to incarnate?
In a word, no. According to Jesus Himself He rightly said at John 1:18, "No one has seen God at any time. The only begotten Son, who is in the bosom of the Father, He has declared Him." And at John 6:46, "Not that any man hath seen the Father, except he who is from God, he hath seen the Father."
John 4:24 states, "God is spirit, and those who worship Him must worship in spirit and truth." In other words, God is a spiritual being and as noted God the Father cannot be seen.
God's Son, Jesus Christ is the one and only Son of God as in there are no others. (John 3:16). Since this is true Jesus as the Son of God shares the same nature as His Father. Jesus did not have a biological father. On the other hand, Jesus also identified Himself as the "Son of Man." On His mother's side He has the same nature as His mother which is human being.
So Jesus Christ has two natures, one on His Father's side and one on His mother's side. It's a universal law that all sons share the same nature as its father. Philippians 2:6-8 teaches that Jesus Christ who always existed as God took on another form which was that of a bond-servant/man. Philippians 2:8, "And being found in appearance as a man, He humbled Himself by becoming obedient to the point of death on a cross."
At John 14:8 Philip said to Him/Jesus, Lord, show us the Father, and it is enough for us." Vs9, Jesus said to him, "Have I been so long with you, and yet you have not come to know Me, Philip? He who sees Me has seen the Father, how do you say, Show us the Father?"
Jesus here is not saying that He is God the Father, look at vs10, "Do you not believe that I am in the Father; and the Father is in Me? (Please notice two persons are in view here.) The words I say to you I do not speak on my own initiative, but the Father abiding in Me does His works."
The point of this is the fact that the Father has no separate manifestation from the Son. The Son is the only manifestation and revelation of the Father. What is known of the Father is revealed through the Son. To see the Son is to see the essence of the Father. Please read John 1:1,18; John 10:30; John 12:45; Colossians 1:15; Hebrews 1:3.)
Everything Jesus did was to please His Father and to glorify the Father. This also means that we are to follow Jesus' example in our daily life. Goin back to Philippians 2, notice what the Apostle Paul states at verse 3-5.
Starting at Vs3, Do nothing from selfishness or empty conceit, but with humility of mind let each of you REGARD ONE ANOTHER AS MORE IMPORTANT THAN HIMSELF." Vs4, do not merely look out for your own personal interest, BUT ALSO FOR THE INTEREST OF OTHERS."
Vs5, "Have this attitude in yourselves which was also in Christ Jesus." I already went over the verses that follow. The point is to follow the example of Jesus Christ and honor Him just like were suppose to honor the Father. (John 5:23).
We must consider the natures of both God the father and that of Jesus in order to understand, not only your question, but also to understand the relationship between the three who make up the Trinity.
John 5:19 KJV Then answered Jesus and said unto them, Verily, verily, I say unto you, The Son can do nothing of himself, but what he seeth the Father do: for what things soever he doeth, these also doeth the Son likewise. Joh 5:20 For the Father loveth the Son, and sheweth him all things that himself doeth: and he will shew him greater works than these, that ye may marvel.
The one commonality between the Trinity is that they are all Spirits.
John 4:23 But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him. 24 God is a Spirit: and they that worship him must worship him in spirit and in truth.
When Jesus conversed with the other two in the Trinity, They conversed in the spirit. Therefore; when Jesus maintains that he could do nothing on his own; what he was alluding to was the fact that being spiritually bonded together all things were from the tripartite God.
Matthew 12:28 But if I cast out devils by the Spirit of God, then the kingdom of God is come unto you.
Note that Jesus said he cast out devils by the spirit of God.God works in the Spiritual Realm; and we too often think of things in our earthly concepts.
Hope this helps