I usually only pay attention to the fast stochastic (I pay little to no attention to "crossovers"), and I use a look back period determined by the instrument's current ATR. For example, I may currently be using a 5 period look back on the ES intraday, but next week it might be 2 or it might be 12. I pay little to no attention to divergences, and I do not use an oscillator to determine trend. For my automated systems, for example, trend is always defined in terms of price relative to one or more moving averages. I will use the oscillator to program the timing of the trigger.
I use to use more indicators when I traded all day, but now that I trade so little, I use moving ave and volume. Plus, I only trade two markets now then few years ago. Yes, waiting for the crossover on stochastic is often late. I like to see "thrust" bar that is completely beyond moving averages to define trend and that often changes slope of the moving averages, so I also use slope and will also use close beyond last pivot.