The only times I have experienced what I would call a ‘second wind’ has been on very long endurance experiences. The feeling of settling in to a comfortable pace after the initial discomfort of exertion I have always considered something more mundane.
I have done a lot of long, hard ski tours. Long days of hauling a big pack or sled gaining elevation. Some long day trips where we covered a lot of terrain and vertical also. I have found often that late in the day, when normally we would be back at camp already and I am felling pretty drained, I have been able to pick up the pace and plug along to the goal. Simple, energy rich refreshment helps, usually by this point I am down to mixed nuts or trail mix that is always in the pack as a reserve. Lots of water too. I believe it is a combination of mental and physical adjustments. You realize there is no choice of stopping, you have to get to your goal, and any rest is really just going to delay that. I assume the body has to make adjustments past its usual schedule and reserves. Probably well past fat metabolization and into consuming muscle tissue by that point. All I know is I can get to a place where I can continue at a good pace for a few more hours long past my usual stopping time.
I remember one long and spectacular day mid season when we were very fit and did a day trip over the Illicillewaet Icefield, down, and back. Thirty plus kilometers and a good 3000 meters vertical. On the way back it had gotten dark, we were dead tired and considering a miserable bivouac - an excellent deterrent to stopping. We took a quick break, watered and fueled up and started again at a recovered pace, found our morning tracks and made it to the top of the glacier in little over an hour. As we suited up for the descent the moon came up and we had an absolutely fantastic run down through great snow. It seemed effortless, and the last few kilometers back to camp went quickly. Then we slept hard.