ramrocket, if you're going to enter trades on the H4, you will want to be checking the daily charts, and it looks like you understand that. But in addition to the stochs on the daily, you also need to look at the moving averages to be sure that they are confirming the direction of trend that you think exists. Don't be affraid of checking an even higher timeframe either.
If the stochs are in an overbought/oversold area, just be aware that they may drop out any day. I think the best time to enter a trade would be when the MA rainbow confirms trend direction, and both the timeframe you're trading and the two timeframes above that are all about to break out of the respective overbought/sold area.
On your GBPJPY chart, yes, the daily is oversold and the MA raindow is down. On the WEEKLY chart, the pair is bullish for the MAs, but we broke a previous weekly low with last week's candle. Also, the stochs are very low. As far as the weekly goes, we could be on the verge of trend reversal, or we could be creating a bottom right now. Does this matter for trading the H4? Maybe.
Try it, record your observations and what happens, and learn from your mistakes. I don't think I feel confident enough to trade the GY with this system in the GY's current condition, and I'm perfectly fine with that, as there are many other pairs.