Is there anywhere in the Torah or Mishnah that talks about the wearing of a tie? I’m interested only in that particular garment. Anywhere it / they explicitly mention the requirement or prohibition of wearing that garment? If so, are there any rules relating to it?

The tie does not appear in any of the early sources as it did not exist as a garment in the olden days. Since the tie appeared as a garment the Poskim deal with a few issues that have to do with the tie, For instance – Can you tie it on Shabbat since tying is a torah prohibition? (Yes, under some conditions) Can you wear it out of the boundaries of Shabbat or in a public domain since it does not appear to be a garment? (Yes, Igrot Moshe OC 3; 46) The Poskim deal with the mitzvah of Keriah – tearing the clothes of a mourner; can you fulfill this requirement with tearing the tie? (No, Sridey Esh B 96) Is wearing a black tie for a funeral prohibited as a non Jewish practice? (No - but better not to, Yabiah Omer 3 YD; 25)