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To my knowledge, Gregory has never granted an interview on his mother. I found it curious, but maybe he's just too private a person. Actually, Tim hasn't really given many interviews, either. Like you, I read Beverly Linet's book in which Tim was interviewed by her; and he did do an on-camera interview on the 1998 A&E Biography of his mother, but other than those, I'm not aware of any other interviews he's given.
From time to time, he has appeared here on Ginger's great Susan Hayward website, but more often than not, he has spoken of his -- and his mother's -- alcoholism.
In a recent post here, I got the impression Timothy was planning on writing, or was starting to write, a memoir. If it's true, I wonder if Gregory will be a collaborator on the project?