Wait so which day was Taluy Behergesh?
Birthdays, Yimei hilula, 5 Teves, etc.
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The תלוי בהרגש was exclusively with regards to Gimmel Tammuz.
The "dilemma" was that on the one hand it was the beginning of the F.R.'s Geulah, on the other hand he was exiled to Kostroma.
The exact answer was: "הדבר תלוי בהרגש, ומזה גופא ששואל, סימן שאין לו הרגש".
["The matter depends on feeling, and from the very fact that he asks, is a sign that he has no feeling."]
Reb Mendel Futerfas would famously declare, "How can one say Tachanun on such a day".
Birthdays, Yimei hilula, 5 Teves - it is pretty clear that we say תחנון on all of these days .... besides the Rebbe's birthday of course