Although I would have to dig to pull out the sources that I have seen over the years on this subject, they all point back to the same source.
The gartel corresponds to the אבנט worn by Aharon HaKohen Gadol and all regular Kohanim during their service עבודה.
The tradition is for 32 windings corresponding to the place it is worn, at the heart לב. If I recall , this appears in the commentary of Rabbeinu Bechaye.
That implies for most people a gartel length that is twice the width of your body or approximately 64 amot. This means that it is actually more like a cummerbund that covers a wide area from the base of the sternum, where the heart is located, to below the navel.
The Avnet also corresponds to the בריח התיכון of the Mishkan which passes through the center of all the planks of the Mishkan, (Shemot 26:28) binding and unifying them together as a dwelling place for G-d’s Presence. This is discussed by the second Lubavitcher Rebbe in his discourses pertaining to Rosh HaShanah, Yom Kippur and Sukkot.
And this is also related to the Jewish King, who binds the entire nation together as one and is compared to the heart of the nation by Rambam in the Mishneh Torah, Laws of Kings and their Wars.
In that context, the entire Jewish people are called a Nation of Priests ממלכת כהנים like Shemot 19:6 which is why the Avnet is a traditional Jewish garment worn particularly during prayer עבודה שבלב.
The cummerbund style of the Avnet also pertains to the length of the straps of the Tefillin shel Rosh. That the right strap, which corresponds to the aspect of kindness is longer (even down to the floor), like the idea of רב חסד in the 13 qualities of Mercy and the corresponding phrase כי חפץ חסד הוא recited during Tashlich. While the left strap, which corresponds with Severity גבורה and judgement דין, is shorter (but is required to extend beyond the neck, corresponding with harsh judgement like פרעה, קשה עורף ומצרים, to reach to the chest), meaning the base of the sternum, the place of the heart. In other words, G-d’s will (רצון היינו נוצר חסד) surpasses and overturns the restrictions (המצרים) of harsh judgment (דין וגבורה). This is the very core of concept behind Yom Kippur and the Ne’ilah prayer.
This relationship between kindness and judgment is like is expressed in the third of Ten Commandments prohibiting idol worship (יתרו כ:ה-ו) And in this way, the end of the shorter, left strap is often tucked in from above into the top of the Avnet, while the end of the longer, right strap is tucked in from below at the bottom of the Avnet.
I believe this is mentioned in Sefer Mishnat Chassidim by Rabbi Emmanuel Chai Rikki, zt”l.
I do not recall anything specific about securing the ends of the gartel beyond the normal concern about not tying fixed knots on Shabbat.