I'm not exactly a jet guy (yet) although I own some stuff that I intend to fly one of these decades. However I am an aero engineer and I do or have done stability calculations for everything from gliders to missiles, even canard fighters.

The upright/inverted method works for aerobatic planes, with basically straight wings. This is a quick measure of how far in front of neutral the CG is for a plane. For a good aerobat with a plenty big tail, you want it almost neutral. That way it goes where you point it and you don't have to fight to keep the plane at an attitude. Having little elevator trim to keep the nose up means you don't need much down elevator when inverted. It also indicates that the CG is very close to neutral balance.

It would not work for any or every jet. For conventional configurations, it might work. L-39 or MB339 with straight wings and tail may behave like aerobats. Doing this with F-16, F-4, canards is asking for trouble. With these, they may behave well at med-high speed, but then would pitch-up themselves when you raise the nose. That is the definition of unstable. They do not have the linear stability response that 'square' airplanes do.

The dive test is also not really applicable. This is developed for gliders. They are also trying to have minimum stability, just a little more than the aerobat. With a dive test for a jet in landing mode , you would want a quick but groovy recovery to a trimmed approach path from a 45 deg dive. Same if you are throttle off on approach and bump a little up elevator then back to normal. You want the nose to quickly and solidly return to the normal approach attitude.

Mainly, Enrique has it. Watch for pitch-up at low/approach speeds.