Counter to this, it's become more of an anachronism than it was 15 years ago. Some summary stats:
Bearish or bullish signal being "right": 57% over the last 10 years. Close to a tossup.

.9% Avg bearish period return (Russell 2000) since dawn of tracking time (1979 in Zeelotes' NSB sheet)
6.7% last 10y avg bearish period return

10.23% Avg bullish period return (Russell 2000) since 1979
3.90% last 10y avg bullish period return (thanks to Covid & the 22 interest rate spike happening during November-May

Total return if you stayed invested (in Russell 2000) and ignored this indicator the last 10 years:
144.42%
Total return if you went to cash during the bearish periods: (Assuming ~2% tr over each of those)
68.65%

(these periods are not exactly the strict June 5th to 2nd week October boundaries, but more late April to mid-May depending on MACD per the old Seasonal Timing System.)