The whole saga began in the early 50s with the (single engined) N-102 Fang, Northrop's entry in the welterweight fighter competition won by Lockheed's Starfighter.
Having lost that, they turned to a lightweight fighter for the USN (because there was never going to be a carrier version of the F-104). But to get it onto the escort carriers (and to a lesser extent the SBC-27A Essex) it had to be smaller and lighter. Here's the first problem the N-102, like the F-104, used a single J-79, the size of which limited how physically small the aircraft could be. But the only smaller engine to the 40"d./10,000lbf J-79 was the 20"/2500lbf J-85. Even two of them meant either too lightweight, or slightly underpowered. So the resultant N-156/F-5 was a little too lightweight.
Not only an US problem. There were many promising lightweight fighter designs at the begining of the 60s just needing a 30"/7000lbf engine that didn't exist. The Brit Orpheus came close, but with only 5000lbf it was no improvement on twin J-85s.
That was the Tigershark's time, if it had been built then, with no F-16 competition, it would have been the export F-X.
As it was, 10 years later, the only likely launch customer was Taiwan, which neither the Carter or Reagan administrations were willing to deal with for fear of offending the PRC.
Right aircraft, wrong time
I’m sure your early history is correct, as I knew there had to be a reason for the strong aversion to a single engine (thanks for the lesson).
However, one reason that T.V. went single engine is because he didn’t want just another “F-5 looking” upgrade. Just another variant. The funny thing was that the F-20 (the three that were made) was made from the F-5 airframe with a different aft section for the single engine.
We were flying the F-16 and Jimmy didn’t want to export our premier front-line fighter, but Reagan didn’t mind selling it to our allies. After that, it became a tough sell.
After we lost the fly-off to General Dynamics and the F-16 (those sneaky bastards offered two different proposals to the Guard. If I recall correctly, one was a new F-16 variant, the F-16C? at 20 mil per copy to our 16 mil and an upgraded F-16B taken from current inventory (they had already been purchased by the gov) at only 2.2 mil per upgrade - numbers may not be exact) a general in the Air Force told T.V. Jones, “Don’t come to the party if you weren’t invited.”
Regards