I believe the incident you refer to is when John Leeming shot down an A4 using his 30mm Aden cannons.
John was an ex-Lightning pilot who had done the "very" short Sea Harrier course and then come down to the South Atlantic onboard the Atlantic Conveyer. He and several others flew onboard HMS Hermes just before the AC was hit and sunk in an excocet attack by Argentinean Super Etendards.
The story goes that John found himself behind an A4 but had neglected to switch on the power to his missile system prior to entering combat and, no matter how much he was pressing the missile fire button, nothing happened.
Glancing down into the cockpit he recognized the two cannon switches which were, apparently, similar to the Lightning's and smashed them into the on and live position. He then closed to less than two hundred yards and opened fire in a long continuous burst. The A4 literally disintegrated in front of him and he flew through and, luckily, survived the fireball!
I have no idea what he "felt" afterwards. John was killed in a mid-air collision not long after returning from the Falklands so he won't be able to tell you in person.
I doubt you will get much response regarding this question from real fighter pilots who have shot down and killed real people. It is hardly an emotional response most of us would like to talk about. I heard someone once said that killing another human being is the ugliest thing you will ever do and, from my point of view, this is pretty close to the truth.
ES