Skinnerton's The Lee Enfield is (A) huge and (B) does contain limited No4 T info. However, the "best" I've found is Peter Laidler's (with Skennerton) An Armourer's Perspective: .303 No. 4 (T) Sniper Rifle. I think I got mine for $30 on EBay. You kind of have to read it with a highlighter to gather together all the specifics of what makes a real sniper, but it pretty much covers everything. Markings you'll have to get familiar with (without repeating what you can find here and on other websites) are the markings wrist "TR", receiver proper "T", stock "S51", receiver "S", inspectors crown, butt stock scope number and, if removed, the hidden butt stock number. There are some exceptions for rifles that never got a scope and such. Rear sights, front sights, sling swivels, etc are also important but replaceable.
Good luck! I'm sure we both wished we were into these 20 years ago when Forum members were getting sets in the transit chests for peanuts!