Interesting and very valid issue! In my opinion the answer is…it depends!
As a general rule, I would always wait to see a close before declaring a valid breakout, as @mtb_rex says, but that also depends on the TF one is talking about! For example, an intraday close above a line on a 4H candle is still an open price on the current Daily candle. Also, the length and shape of the candle gives some indication of how powerful the breakthrough has been…
The distance for a breakout, I think, also depends on the timeframe one is trading. If a trendline is drawn on a daily chart and stretches back a long way then a step over the line of 10-20 pips is not really very meaningful at all. But if one is trading a 5min chart then 10-20 pips is already a good move! (but trendlines on such short TFs are not really “trendlines” as such they are just the result of a lot of technical daytraders looking at the same thing and causing some intraday wobbles!
Personally, I look for context/confluence in other areas. For example, if we see a spike down through a trendline but my 1H setup is still positive with respect to my 4H then I would wait. But if my 1H was already down through my 4H setup then the spike would confirm the direction and I would look for an sell entry.
I also need a clear definition of when I am wrong, and in this situation it would be when/if the 1H setup reverses back into synch with the 4H.
But, actually, although we talk a lot about where to enter trades, in my opinion the biggest and hardest challenge, that really does determine the optimisation of our trading is when to get OUT of a trade!