I have seborrhoeic scalp eczema - the only thing that works for me is washing my hair daily and blow-drying it minimally at the roots, but better everywhere until mostly dry. I still get some flare-ups, but it's nowhere near as bad as it was years ago, when I actually had no idea that it's a proper skin condition with a name and not just an itchy scalp that I scratched to bleed every day and flakes
Products I like:
Ketozolin shampoo - the best, and doesn't smell horrible
Selsun shampoo - also is great and really helps immediately with the itch, but the smell of sulfur is strong. I'm only using Ketozolin these days
Wofacutan shampoo - very gentle shampoo with a tiny bit of sulfur, doesn't smell at all and doesn't dry out. They also do a lovely shower gel also for skin conditions designed to be very gentle and help with itching.
Generally, I need to use a shampoo with SLS at least weekly, more often is better, I can't just rely on SLS-free shampoos as that guarantees an eczema outbreak. I also make sure to always put a bit of the foam behind my ears, as that is where it threatens to spread. I really focus on washing my scalp, not my hair.
With these "tricks" my scalp is mostly okay and I only get a handful of flares during the year. My scalp is also naturally very oily, so I probably would wash everyday anyway even if I didn't have this, I look just too greasy for my liking. But it's okay for me, I like the feeling of freshly washed hair and it's a quite cheap way to deal with eczema, it doesn't need much more than a regular blast of shampoo these days.