“There is a book on the table. The book is brown. I will accept the book exists. But does the colour brown exist?”
Brown is a wavelength. White light bounces off the book. The characteristics of the book absorb certain wavelengths. What is not absorbed is reflected. Let us call this isolated, reflected wavelength (low-intensity light at 600 nanometres) which reaches our eyes “brown”. The eyes, which are receptive to wavelengths, transmits that information from the retina down the nerves to the brain where it is equated to “brown”.
You see the book. I see the same book. The colour which is reflected corresponds to “brown” in your vocabulary and my vocabulary. But whether we see the same colour in the same manner does not matter. As long as we are talking about the same “thing” is all that is important.
In this sense, we have isolated the property “brown” to be the wavelength and given it this agreed-upon name. The wavelength exists as light, as energy. I would say “yes”, it physically exists.