I checked the "Turn-of-the-month" effect ... a historically useful enhancement whose advantage has weakened after 2020.

I have read studies that said the best day to trade is at the open on the last business day of the month.

Now I have come to think that any such findings are just statistical noise.

When looking at the trading-day-of-month for any historical period, there will be ONE that's best. That's just how randomness works. One will be best and one will be worst.

Also, there is a lot of randomness just in the trading day. Our backtests don't capture that.

Case in point: The other day I was looking to buy LITE. It opened at 870 with a pretty wide bid-ask spread. I put in a buy limit order at 880. Which did not fill, so I bumped my limit up a few times to try to get a fill inside the spread. My last bid was 903.
LITE continued going up to the day's high of 977!

Given all those observation, I now think that that we are just seeing a pattern in randomness.
Just pick a trading day that is easy.

For most people the easiest is probably:
* Run your screen picks during the weekend after the last Friday of the month,
* Do your trades at or near the open on the upcoming Monday.

* Of note, market (not limit) trade orders placed during market close will execute at the open. Similar to market-at-close, all buy & sell orders fill at the same price. You can place your sell orders during the weekend and then do your buys after the market opens.