Is there any source for the practice of not only dipping one's fingers into the Havdalah wine that was used to extinguish the fire and rubbing the eyes with it, but also spreading it around onto other parts of the body, and/or clothing, such as the forehead, the back of the neck, pockets, and any place with aches and pains?
Not sure about sources for most of these (although see Madeleine's comment to the related question).
But about the back of the neck, it may be related to the idea that this is the location of the luz bone (specifically, the protrusion where the knot of the head tefillin is placed - Arizal, Likkutei Torah to Judg. 4:5*); it is from this that the body will be reconstituted at the resurrection of the dead (Bereishis Rabbah 28:3). There are various opinions about what food (if any) the luz is nourished by; one is that it is from the havdalah wine (Maavar Yabok 2:6). So someone may have gotten the idea that some of that wine should be applied to the luz directly.
* Although several Rishonim (including Aruch and Rashi) identify it as the vertebra at the base of the spine.
I have a book with all the Libyan customs- Nahalat Avot and on pg. 74 it brings down this custom. However, some of the sources are unavailable. However, this book has a Haskama from: Rav Ovadia Yosef Shelita, Rav Mordechai Elyahu, Rav Eliyahu Bakshi Doron, and Rav Shelomo Amar.
The source for putting the wine on one’s eyes seems to be Pirkei d’Rebbi Eliezer ch. 20:
רבי אליעזר אומר: לאחר ששותה אדם כוס של הבדלה, מצוה להטיל מעט מים בכוס של הבדלה ושותה כדי לחבב את המצות. ומה שישאר בכוס מן המים מעבירו על גבי עיניו. למה? משום שאמרו חכמים, שיורי מצוה מעכבים את הפורענות.
R’ Eliezer said: After someone drinks the cup of Havdalah, it’s a Mitzvah to put some water in the cup of Havdalah and drink in order to make the Mitzvos precious. Whatever is left in the cup from the water he should pass on his eyes. Why? Because the Sages said, the leftovers of a Mitzvah prevent punishment.
It seems that the bit about water got left out over the years, leaving putting from the cup on your eyes. The Rema’s wording in OC 296:1 seems to echo this idea:
ורוחצים בו עיניו משום חבוב מצוה:
We bathe our eyes in [the Havdalah wine] because of the preciousness of the Mitzvah.
using the same reasoning the Midrash gives for putting the water in the cup.
Shulchan Aruch 296:1 brought by the Rema as a way to show that we cherish the mitzvah (this goes just for the eyes, I think that the others are built on the explanation of the Rema that we spill for to have a Bracha for the week to come so maybe people target those things needing a bracha.)