Although I’m not the type of guy who thinks twinkly LEDs will enhance his apparel, one of Mary’s quilting thread sources had a closeout deal on their “wearable electronics”, including a large cone of stainless steel thread / yarn:

… CR2032 lithium cells & holders, plus assorted LEDs on small PCBs.
The usual advice for connecting the thread seems to involve knotting it through the PCB holes, then sewing it to the backing fabric. Alas, I’m bad with knots and the stainless steel yarn isn’t all that cohesive:

The holder has an even smaller hole, but Mary gave me a needle threader that helped:

Some advice found on The InterTubes suggests using copper crimp beads (perhaps with solder) to prevent the thread from completely unraveling and keep the thread loop tight around the PCB hole:

Beadworkers use crimping pliers that leave a tidy dent; I mashed the beads with a needlenose pliers and called it good.
The LEDs seem to be white LEDs with filters or, perhaps, blue / violet LEDs with different phosphors: their forward voltages look more blue than red or green. Everybody in this field depends on the minor miracle that lithium cell voltages match blue LED forward drops closely enough that you can get away without a ballast resistor.; the cell’s 20-ish Ω internal resistance doesn’t hurt in the least. An interesting white paper (SWRA349) from TI explores the effect of current on cell capacity and how to size a parallel capacitor that reduces the peak battery current.
The black gunk is Wire Glue, which costs about five bucks for a lifetime supply in a small jar (or nigh onto 15 bucks via Amazon Prime) and is basically carbon powder in a water-based binder. Apply a dab to the connection and the water evaporates to leave the carbon + binder behind.
That works better on joints that don’t move, which is precisely what you don’t have in a wearable electronic situation. You can see the crumbling Wire Glue after the trip back from a Squidwrench meeting:

I also picked up a Permatext Rear Window Defogger repair kit (09117, if you’re looking) that seems to be a staggeringly expensive way to get a tenacious high-current conductive adhesive. More on that later.
The yarn runs 3.5 Ω/ft, much lower than Adafruit’s three-ply yarn (10 Ω /ft), and suggests itself for flexible connections, EMI gaskets, and suchlike.
Those LEDs are taped to the kitchen window, where they cast a cool light over the table, with the battery holders sitting on the sash. I’d just replaced some data logger CR2032 cells, so they’re running from nearly dead lithium batteries.
For future reference: 2.77 V and falling, pushing less than 2 mA through the LEDs.
Radio Shack (and others) offer a conductive glue. The product description on the Radio Shack site includes the lovely phrase “the conductive performance quality is choiceness”.
What could “a single component, inorganic aluminosilicate material, in black” possibly mean, given that it’s “graphite-filled”? I count three materials, right there…
Most likely, it’s relabeled Wire Glue at an even higher price.
You may wish to consider the buntline hitch, which is supposed to be self tightening under load http://www.animatedknots.com/buntline/
Phew! That must’a been about where I fell off the Boy Scout path.
Given that I must manipulate the thread using tweezers, anything more complex than an overhand knot lies well beyond my skill set.
Mashing a copper tube, now, that I can handle!
Curiosity, what is the diameter of the stainless steel thread ? Any idea on the resistance ?
Overall and lightly squashed, the two-ply yarn is 0.35 mm = 14 mil.
Each of the gazillion strands is maybe 0.03 mm = 1 mil and, absent some serious fixture & measurement effort, I have no idea what its resistance might be. Heck, I can’t even count ’em!