OK, so I've had Toula, Irish Wolfhound adoptee now for 2 years. She's a terrific dog, but has finicky eating issues. For the most part, I have her figured out - what food agrees with her, what I need to add to make it yummier!, and not to get upset if she walks away as she usually returns to finish it. (This has been confusing after owning labs for 20 years!)
Although she wasn't trained very well before I got her, I think her previous owners (who cannot be found) gave her a signal when it's okay to eat, after you put the bowl down. Something I've done myself in the past.
I usually use "OK!" But she will still hesitate when I'm next to her - looking at me like she's waiting for me to say the right thing. I've tried other stuff - "go ahead", "good girl", "eat", but she'll just look at me like "You, dummy, you haven't said it yet!"
My Saluki is also a finicky eater and I've had her all her life. Like you, I've about figured out what she WILL eat, but WHEN she eats, and how much is totally up to her.
I think it may be just a sight hound thing. Many of them are not 'chow hounds'. This is my 4th Saluki over the years, and none of them have been eager eaters, but Mira is, by far, the most finicky. She was dominant over both her dam and my old Dobie but didn't bother to keep either of them out of the food bowl (her dam was somewhat picky too, though she got better as she aged, but not the Dobe who ate with the relish of a 'regular' dog, lol). After I lost the older dogs, Mira mourned for over 18 months ... getting her to eat was a nightmare. Now she's doing much better, but still doesn't eat as much as I'd like for her to ... and definitely only when SHE'S ready.