Greater fool theory is something my friend Dr Elder talks about in his books, seminars and camps. It relates to his short-term trading method. His philosophy of buying value is very similar to mine except he uses only technical analysis, whereas I also use fundamental ratios. So, we are both looking to buy value and sell to the (greater) fools. The difference between what we do is the time frame. Dr Elder may hold a position for hours or days. I hold a position for months or years. I may even buy a stock from him if he was trading one I was interested in, because in his time frame it was above short term value, but in my time frame it was undervalued. The result may be that I hold the stock for a couple of years. Dr Elder may buy and sell it many times in that period. We would hopefully both make money.
So, if a stock is on my list to buy, greater fool theory is not relevant, because over-valued stocks never got to first base in my stock-selection method. For it to drop off my list of buys it would have to move a long way or announce some bad news. Then I would reassess.
Where I think your questions are coming from is should you chase a strong stock? As I have said earlier, the answer all depends on what you are trying to do.
However, for me, I love the ones other people will not buy. Right now we are in the fourth year of a bull market. As stock that is still undervalued and moving up strongly is a prime target for me. I will chase it and buy an initial lot. Then if it keeps racing away, I am on board and laughing. However, most likely there will be a correction, when I buy more and then a new high when I complete the building of my position.
The alternative at this stage in a bull market is that a stock is only now poking its head out of an accumulation pattern. I may buy this one too, but if it is not moving strongly and presents a turnaround story, it is a dog that has been asleep while everything is happening. Yes, you can buy it close to the lows of the chart. Yes, you may do really well with it. But unless it is a special case, dogs that wake up three years late and show little signs of life should be left to go back to sleep.
Conclusion: Buy value. Buy strength. Leave the dogs to the lesser fools.
That is my philosophy and it works for me. But you are not me and may have quite a different approach. There are many ways to make money in the markets. What you need is to find one that fits your temperament, not search for perfection. Perfectionists do not make good investors or traders, but that is an issue for another day.