[Occasionally6]

It is part art, part science. You use the science to develop the art. You do basically have to do it to learn it but knowing the theory helps.

Do hold the rpm at the matched speed. A shift is pretty fast, some fraction of a second, so you're not (usually) sitting with the rpm at a particular speed for even seconds - although you could do so if you wanted to.

If you simply "blip" the throttle and then time the shift lever movement to when you pass through the "right" rpm, you might match the rpm at the start of the shift or some point during it but you can never do so all the way through the shift. Because it is very difficult to get the rpm match exactly right anyway, it may make little practical difference. I think it is better to learn the right way - and to understand - from the start.

If you don't have the clutch engaged (in neutral) when the engine revs are matched, the input shaft and new gear speeds aren't being matched, just the engine and wheel speeds. The synchromesh is still working away to do that for you as you make the new gear selection.

A down shift will still be smoother because you aren't sucking energy from the car into the engine rotation. It's also easier on the clutch. It's OK as a valid driving technique but it's not full rev matching.

It is faster than double de-clutching because you don't have to pause and pump the clutch in the middle of the shift. Like I said, it is a valid technique.

If you are starting from a neutral coast situation with the engine running, whether after bump starting or not, there's no valid reason not to rev match before depressing the clutch. And reason to do so.

A comment on accelerator pedal movement: It is quicker to move the gas pedal past the position that would maintain the required rpm and then come back off it as the rpm rises to the desired level.