He is going to cut the part of hair (that) he dyed purple a few months ago in a barber shop.
I bracketed that cause it seems like placing that is optional,
if I omit the relative pronoun in this sentence ,
does he dyed purple a few months ago still act as an relative clause?
If we have that here, I can easily understand that:
He dyed part of his hair purple in a barber shop, and he is going to cut it,cause the PP in a barber shop belongs to the relative clause.
But if we don't have that in the sentence, will the meaning of the sentence slightly change? By which I mean would another interpretation appear without the presence of that?
Another interpretation could be: Part of his hair is dyed purple a few months ago, and he is going to cut it in a barber shop?