I've been doing this for decades but never knew it had a name. For the best splice, use the Western Union splice. You can use it for more than one connection, too.
To really dress it down smooth I hold one side with needle nose pliers and then Gently work the curved needle nose pliers, spinning them and working them down one end of the splice, swap ends and smooth the other end, hit it with some flux and solder it up.
When you can get the solder to flow and the whole connection has solder in it,but you can still see the shape of the wires,it's done.
Look up Western Union splice and hit images.
And Put the heat shrink on before you solder it..
You know you don't need to ask why I would mention that.

Yeah, that is the Tikkit.
I wish I had command of the language sufficient to explain that so the student would get it and I would not have to type so much. It's not exactly a thousand words, but the picture sure eliminates them.
Thanks for dragging that in here.

Thats how I usually solder, but lately I've been realizing that heat shrink is a pain in the ass, so I resort to electrical tape. Not as elegant, but most of the time its easier to deal with.

Here’s my tip for cleaning the tip. After each connection I push the tip thru card board box twice before applying more solder to the tip , it removes the garbage from tip and leaves a professional look. Caution the box may smolder or catch fire , but the tip looks like chrome.

That’s all a pia , try it you’ll never go back.

Thanks to all for the cool soldering tricks.  That Western Union Splice looks bullet proof.

A clean tip is needed for a professional solder joint. Solder then clean , solder then clean , every time ! My other , ok let’s say hobby is hot rodding electric guitars , every connection has to be perfect and stand the test of time. I only use a rosin core 60/40 or 40/60 (have CRS) made by Kester. Absolutely the best solder to use on anything electrical. So clean the tip every time you’ll see the difference.

I've never needed to work on anything that sophisticated. Wiring, auto,bike, clunky stuff that gets volts and moves amps. Messing with a guitar pick up? Yeah, now you're in the neurosurgery end of soldering. What do they transmit? Milliamps? And if the connection is the least bit resistive, it sounds crummy? I've never had one of those DialAWattage nifty stations. You are right about those Weller low temperature welders. Too hot for most stuff, even on the first c!ick. If I'm working on something that has a PCB, I get the switchable 15-30 watt iron. Years pass between uses. So that means twisting on the tip,cleaning up the connection, snug it up get it hot,stab it in the flux, retin phhht,, Only when I Hafta..
I'd be happy to watch, but sounds like the work you do is pretty persnickety.
The little torch has been used outside, like on a pickup to trailer ,,that is the extent of my work on pickups.

Sounds like you should do the explaining.