The only thing we have done is a skin scraping. Nothing showed up.
We could do some bloodwork and/or a biopsy, but her vet isn't in a rush to do anything at the moment.
Melanocyte alopecia and zincc responsive dermatitis have come up, but definitely no diagnosis right now. I think she is losing some hair on her ear too.
If we have unlimited funds, I'd probably choose to biopsy or do a ton of bloodwork, but she doesn't appear to be in danger, so we are just watching it. A derm consult also wouldn't be a bad idea, but no rush here...
I hope your vet figures it out.
BTW, Ellie is usually itchy to an extent and she rubs her face, but not enough to cause anything like this.