Chronology of the cot-caught merger

The cot-caught merger often coexists with the father-bother merger. Although it can be found in regions like Eastern New England, which lacks the second merger, the other dialects exhibiting the merger also exhibit the second merger. In many non-merged dialects, the vowel in caught is still a low vowel (specifically [ɒ(ː)]). It seems that the origin of the cot-caught merger in most dialects having it was facilitated by the father-bother merger (the merger of the LOT (/ɒ/) phoneme into PALM (/ɑ/)), which freed up space for the THOUGHT vowel to vary from [ɔ(ː)] to [ɒ(ː)], which in turn merged with PALM/LOT to form the cot-caught merged vowel ([ä~ɑ~ɒ(ː)~ɔ(ː)]). That seems to explain why the cot-caught merger manifests different phonetically in various dialects and why the range of the merged vowel is greater in dialects with the father-bother merger than in Eastern New England, which lacks it. So, when did the cot-caught merger appear and by how much it postdated the father-bother merger?