Back2Natural has ASH tones in it that neutralise red tones.
It comes in all sorts of shades and isn't just for black hair.

Your side & back hair is a more neutral tone than the system.
By neutralising the red, it would help blend the two better.
Colour restoring conditioners like Back2Natural & Aufero do 2 things.
They restore colour and they neutralise brassy tones.
So if you only want to remove those tones (but not restore colour) you buy a shade lighter than you need and then it won't make the system darker.

If you do decide to use a dye, I wouldn't recommend using a metal comb as all dyes specifically say not to allow the dye to come into contact with metal as it chemically alters and distorts the colour.
You have to be VERY careful not to get any dye on to the base.