After making that observation that the main difference in the timing parameters is just a 1 month lead or lag in the change of the signal, I started to wonder just what the actual difference were.
And once I started I kept thinking up more ways to look at it. Kept me busy for a couple of hours of Excel work. ;-)

So here's the differences applied to one particular cycle of the P-HL52 screen, from 2/1/1985 to 12/1/2025.
The timings all used the weekly price of ^GSPC (S&P 500).

Each line is the month which has a different signal of the two timings, the (untimed) return of that month, and which timing scheme turned out better for that month.
Better means being OUT for a loss month or being IN for a gain month.
Whiplash is when an IN month is between 2 OUT months, or vice versa, so you are going IN or OUT for just one month.

Also is the number of months IN and OUT, and the number of sells. These numbers are almost identical for all the timing parameters I tested. Demonstrating that, yes, the main difference is the 1 month lead or lag of a signal.

There are 556 month in total.

                                                  # in      # out     # sells
1st -->   64 wk SMA for 1 wks -1% below GSPC      397       100       18
2nd -->   52 wk SMA for 1 wks -1% below GSPC      396       101       19
                                                                      
Date      1st       2nd       ---whiplash---       Mo Rtn    #1 best   #2 best
8/7/1988  out       IN                  WL2       -5.7%     1st       
10/2/1988 out       IN                            -0.7%     1st       
8/7/1994  IN        out                           9.3%      1st       
11/5/2000 IN        out                           -29.3%              2nd
5/4/2003  out       IN                            11.8%               2nd
8/2/2009  out       IN                            -5.2%     1st       
11/6/2011 IN        out       WL1                 2.1%      1st       
1/1/2012  IN        out                           6.1%      1st       
6/3/2012  out       IN        WL1                 6.0%                2nd
1/3/2016  IN        out                           -7.8%               2nd
11/4/2018 IN        out                 WL2       1.7%      1st       
3/1/2020  IN        out                           -13.2%              2nd
3/6/2022  IN        out                 WL2       9.6%      1st       
2/5/2023  out       IN                            -8.5%     1st       
3/5/2023  out       IN                            -2.8%     1st       

                                                  # in      # out     # sells
1st -->   64 wk SMA for 1 wks -4% below GSPC      408       89        12
2nd -->   52 wk SMA for 1 wks -4% below GSPC      410       87        15
                                                                      
Date      1st       2nd      ---whiplash---      Mo Rtn    #1 best   #2 best
8/7/1988  out       IN                            -5.7%     1st       
9/4/1988  out       IN                            2.2%                2nd
10/2/1988 out       IN                            -0.7%     1st       
9/6/1998  IN        out                 WL2       9.8%      1st       
11/5/2000 IN        out                           -29.3%              2nd
4/7/2002  out       IN                  WL2       -11.6%    1st       
5/4/2003  out       IN                            11.8%               2nd
1/6/2008  IN        out                           -13.6%              2nd
8/2/2009  out       IN                            -5.2%     1st       
7/4/2010  IN        out                 WL2       13.6%     1st       
8/7/2011  IN        out                           -4.9%               2nd
1/1/2012  IN        out                           6.1%      1st       
2/5/2023  out       IN                            -8.5%     1st       
3/5/2023  out       IN                            -2.8%     1st       

                                                  # in      # out     # sells
1st -->   64 wk SMA for 1 wks -4% below GSPC      408       89        12
2nd -->   58 wk SMA for 1 wks -4% below GSPC      410       87        14
                                                                      
Date      1st       2nd       ---whiplash---      Mo Rtn    #1 best   #2 best
10/2/1988 out       IN                            -0.7%     1st       
9/6/1998  IN        out                 WL2       9.8%      1st       
8/2/2009  out       IN                            -5.2%     1st       
7/4/2010  IN        out                 WL2       13.6%     1st       
2/5/2023  out       IN                            -8.5%     1st       
3/5/2023  out       IN                            -2.8%     1st       

And finally,

                                                  # in      # out     # sells
1st -->   64 wk SMA for 1 wks -4% below GSPC      408       89        12
2nd -->   64 wk SMA for 1 wks -1% below GSPC      397       100       18
                                                                      
Date      1st       2nd       ---whiplash---      Mo Rtn    #1 best   #2 best
4/3/1994  IN        out                           -2.1%               2nd
5/1/1994  IN        out                           -10.3%              2nd
7/3/1994  IN        out                 WL2       -4.9%               2nd
12/4/1994 IN        out                           0.8%      1st       
1/1/1995  IN        out                           -2.5%               2nd
9/6/1998  IN        out                           9.8%      1st       
10/4/1998 IN        out                           8.6%      1st       
1/6/2008  IN        out                           -13.6%              2nd
7/4/2010  IN        out                 WL2       13.6%     1st       
8/7/2011  IN        out                           -4.9%               2nd
6/3/2012  IN        out                 WL2       6.0%      1st       

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