That will be depend on nut width. "Vintage" is the construction type — single-action truss rod adjusted at heel; one piece necks available; 7.25: radius available, etc.. You can still select modern features, and pick from a 1-5/8" (1.625"); 1.65"; or 1-11/16 (1.6875") nut width.
"Officially", old Fenders were 1-5/8" and old Gibsons were 1-11/16" (many mid-'60s Gibsons were 1-9/16"), but since they were all shaped by hand, they varied greatly from neck to neck. Going by the Blackguard Book, 1950-1954 Teles from 1.60" to 1.69".
I did not plan on this post being purely on averages, but I haved search my office, garage and basement for my digital calipers and I can't find were my teen has put them. As soon as I find it, I'll give exact measurements from my Warmoth 1-5/8" neck.