I've not tried with respect to different sectors, but rather with big/small/mid-cap, and value vs. growth.
Here's a useful set of charts from Ed Yardeni, which I've posted here previously. In my opinion it will give actionable signals from time to time. You need to have a long timeframe, however, like 5, 10, 15 years. I find figures 17-20, and figure 1 to be the most useful.
https://www.yardeni.com/pub/stockmktperatio.pdf
I've made a couple of significant allocation changes based on relative valuations in the past. The most dramatic was in 1999-2000. Large growth was very expensive at the time. A person who recognized this and acted on it did not suffer the so-called lost decade. I sold all of my large growth holdings and reallocated into other assets.
The next significant allocation adjustment was in the wake of the Great Recession. During roughly 2009-2011, big caps were cheaper than small caps, and there was little/no premium on growth stocks. The best investment to make at the time was growth.
Today we are back to a situation where small caps and mid caps are notably cheaper than big caps. All of my 401k money has been in small-cap and mid-cap for two years now. Big caps are not as overvalued as in 1999, however, and to me it's not worth the tax hit to sell the big caps in my taxable account.