I believe that Jesus appeared to the two on the Emmaus road to demonstrate that, risen, he appears and ministers, but in 'another form' (see Mark 16:12). That is to say another form than that in which he had appeared to Mary Magdalene.
She, too, had not realised it was he - at first. But that was a personal appearance, to a single individual. He appears, as risen, to the individual, in a particular way.
But he now demonstrates - to the two on the road to Emmaus - that he will also appear 'in an another form' in a corporate way. To the two, he was a teacher and a minister, opening up the scripture to them both, such that their hearts burned within them at his words.
Yet they realised not that it was he - at first.
So it is with those who minister the word in the ecclesia, the church, among the brethren. At first, they are but teachers of doctrine. But as the word is received and as the heart burns, it dawns upon the hearers, that it is Christ himself ministering - in another form.
That is to say in another form than the individual knows him personally and intimately.
But once it is grasped that the teachers sent by Christ are 'able ministers of the new testament' II Corinthians 3:6, once they appreciate that they are 'ambassadors of Christ' who beseech their hearers 'in Christ's stead', then the form vanishes from sight.
Then Christ is appreciated that he, himself, ministers from the glory, from the throne of his Father, in Spirit, and the form (that is to say the visible teacher) just disappears.
The Lord Jesus Christ, from the glory manifests himself to the individual :
He that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him. (John 14:21)
And he appears (in another form) as he ministers in the ecclesia, the church :
I will declare thy name unto my brethren, in the midst of the church will I sing praise unto thee, (Hebrews 2:12 from Psalm 35:18)
And the form disappears as one realises that it is he, himself. Then one follows such ministers as they follow Christ, not following a man, as such, but following him in the manner in which he, himself, follows the Lord (I Corinthians 11:1).
Then the head of every man is Christ, within the assembly (I Corinthians 11:3) and no man above another : but if any is great among them, he is as a servant (Matthew 23:11).
[All quotations and references are from the KJV.]