Best Sector Time Frames intra? 1 month? 6 months? for long term investing

The variable is not the time frame - there are success stories for every time frame.

Here's an interesting one for very short term trading:

https://washingtonpost.com/business/meet-dylan-the-daytrader/2013/05/09/00786200-b5d6-11e2-b94c-b684dda07add_story.html

Compare that story to Warren Buffet, a very long term investor.

The variable is you - especially temperament, but also skill and experience and what you want from the market. If you need stimulation and frequent payoffs, you want to trade short term. If you like to think things over and plan things out, you want to longer term.

For more on sector rotation:

https://stockcharts.com/search/index.html?q=sector+rotation+model