After looking at opening and closing hours, I decided to split the difference and investigate midday hours: the time in the market from the end of the first hour of trading to the start of the last hour. Going back to March, 2003 (N = 757) in the Dow Industrials, I find 78 occasions in which we had a gain of .50% or greater during the midday hours. The average change to the same day's close was .09% (46 up, 32 down), modestly stronger than the average gain of .01% (403 up, 354 down) for the sample overall.
We had 89 occasions in which the midday hours lost .50% or more. I did not find a meaningful edge by the close of the same day. By the close the following day, however, the Dow averaged a gain of .11% (50 up, 39 down), stronger than the average gain of .06% (393 up, 364 down) for the sample overall.
My overall impression is that intraday traders, like the protagonist in Neil Young's "The Needle and the Damage Done", are milking blood to keep from running out. While there are some historical patterns in intraday markets and over very short time frames, they are modest compared with those that we've seen over swing periods. I'm not sure that's well appreciated among active traders.