Nah, the VT fuses were not "late war" invention, and not for "big naval guns" only, although one might discuss when the gun is considered big enough to be called "big"
. The first american operational Mk 32 fuse for standard naval 5 inch AAA gun was introduced on the Pacific in november '42, with the first plane shot down by it in january '43. Later marks were small enough to fit into 90mm army AAA gun.
From technical point of view, the fuse was based on a kind of a small radar, very simplified of course. Here are some details:
By June 1941, circuit work had been carried to the point where a circuit of sufficient sensitivity and small enough size to be contained in a fuze could be made. The circuit consisted of an oscillator, a two-stage audio frequency amplifier, a thyratron, and an electric detonator developed by Hercules Powder Company connected in the thyratron output in such a fashion that it would initiate the explosive detonation. A dry battery built by the National Carbon Company and similar to the unit used in the 37mm test projectile was used as a source of power. Switches, known as set-back switches and developed by Section T, were used in the fuze to close the battery circuits upon firing of the projectile. An electrical arming delay was incorporated in the circuit to prevent arming of the fuze until after the tube filaments had heated and the unit had quieted down after the initial impact of firing. The oscillator radiated a radio frequency signal. Some of the energy from this radiated field would be reflected back from any target in the vicinity of the projectile in such a fashion as to react upon the oscillator, causing an audio frequency signal which was then amplified by the amplifier and used to trigger the thyratron. The electric detonator in the thyratron output circuit initiated detonation of the auxiliary detonator and hence the explosive charge. At this time development had progressed to the point where a complete mechanical design of a proximity fuze was laid out.
The quote above comes from: Dilley, N. E. "Development of Proximity Fuzes (VT) for Projectiles - VT Fuzes MKS 32 to 60, Inclusive (General Description)." chapter 1 of The World War II Proximity Fuze: A Compilation of Naval Ordnance Reports by the Johns Hopkins University Applied Physics Laboratory. (Silver Spring MD: The Laboratory, 1950): 1-12. [declassified 16 Jun. 1976]. Much longer fragment of it was posted at Ubi forums ages ago, I don't have the link, but copied some of it.
The British fellaz were cooperating in the development program and later they were working on their own fuse, but I admit I don't know much about it!
Cheers.