What was the BVR (Beyond Visual Range) missile fielded during the Cold War again? Ah yes - Phoenix.
The F-14 back seater had a way to "see" BVR, I was told long ago. Could be true.
In any case the scenario the weapon system was designed for was an anti-ship cruise missile attack on the carrier or escorts, air-launched from Russian bombers. Such an attack would normally be first detected and verified by a dedicated flying radar platform, so there wouldn't be much mystery about the nature of the target. The Phoenix could reach out and engage either the Russian bombers or the missiles they launched.