Technically I think it was an IRST: infrared search and track. Same concept as FLIR, but used primarily as a targeting tool for air to air combat as opposed to safe navigation of the aircraft in bad weather/night conditions or air to ground attacks. Some Navy and early USAF (C and D models) birds had them. In later years the fairings were used to mount sensors for the ECM/RWR suite.
When the USAF adopted the gun the F-4 (Navy and Marines never did that, continued to rely on a centerline mounted gunpod) never got a longer nose and smaller radar dish/nose cone. It’s the short fat vs long skinny nose that differentiates the gun equipped Phantoms, not a blister under the nose.
You might enjoy this website. Here's a quote:
The F-4E was the major USAF variant with 959 aircraft produced for the USAF and 428 produced for export. Although the original Model 98B proposed four 20-mm cannons, a design change in 1954 called for a long-range high-altitude Mach 2 interceptor of which only missiles would be required.However, experience in Vietnam with air-to-air encounters showed that this arrangement was inadequate since the earlier Sparrow and Sidewinder missiles did not perform up to expectations. They frequently missed their targets and were subject to countermeasures.
SUU-16 gun pods were installed on the F-4C but the extra drag degraded performance and took the place of ordinance or fuel pods.
To correct this, an internal General Electric Vulcan (M61A) 20 mm, six-barrel, rotary-cannon with 639 rounds was installed on the F-4E.
Due to limited space, a new nose configuration was adopted from the RF-4C reconnaissance version, housing an AN/APQ-120 radar set with a smaller 24.5" x 27.4" antenna and an external pod below the nose housed the cannon.