Short answer: a good accent evaluation is first-language specific.
To better guide you to a different way of saying things, the coach should be on the same page with you. Literally. They should be able to showcase what it is that you do differently that makes you sound unclear or inexpressive. It should be explicit. It should be physical.
To be effective, a coach should know the sound system of your first language (yes, even if they don’t speak it). They should be able to exactly tell what the tongue and lips do to produce the sounds in your first language and how English is different when it comes to that particular sound or stress feature.
A good coach fixes your mispronounced sounds in one, or at most two, classes. After that you’ll need to practice-practice-practice, but you’ll be 100% certain of when you’re mispronouncing the sound and when you’re nailing it.
Good thing is, you know you found a knowledgeable coach when you see one. There’s an easy test. A coach who knows what they’re doing should be able to mirror your pronunciation or stress pattern. If they can’t do it, they can’t help you effectively because they don’t know what you need to change in your oral posture to sound better.
Why is “L” a vowel in Hindi and a liquid consonant in English?
Which two of the four Mandarin tones, in combination, produce the most common American English word stress pattern /\?
Why Russian speakers have a hard time hearing American English stress and how this can be remedied?
If your coach can answer the questions of this caliber, you’re in good hands.
General explanations won’t help you anymore because, as a proficient English speaker, you are way past the time of “Listen and repeat after me! Dog – dug. Ship – sheep.”. You’ve seen it all. You have more experience learning languages than some teachers out there. You need someone who knows how to bridge the gap between the two pronunciations: yours and General American.
Where there is a will, there is a way.
So very true!