Splice connectors such as US-style wirenuts and UK style terminal blocks are demonstrably better in nearly every way to the twist-and-tape method you describe.
- Wirenuts and terminal blocks are more resistant to mechanical failure due to heating/cooling cycles and the mechanical stress of installation.
- Wirenuts and terminal blocks are easier to inspect and test, even long after initial installation.
- Wirenuts and terminal blocks are easier to install CORRECTLY and require less training to do so.
- Wirenuts and terminal blocks can be quickly removed, and can be re-used without shortening the wire.
- Tape can be removed and the wires reused, but the process is labor intensive and messy because of the adhesive. It's easier to cut the wires before the splice, thereby shortening the wires.
So why are wirenuts not more common everywhere? Cultural bias and intertia. For example, wirenuts are not commonly used in the UK because an early wirenut product in the UK market had a design flaw and frequently failed, spoiling the reputation of the product. Terminal blocks became the standard by default. Because of this history, wirenuts are seen as inferior in the UK, when they are empirically not. They are just different than the commonly used terminal block.
I would argue the same is true for twist-and-tape joints in Brazil: it's how it was done in the past, and anything different is strange and therefore must be wrong. The only difference is that, at least for household wiring, wirenuts and terminal block are empirically superior to twist-and-tape splices.
Tape is not a thing for splices. You should not be using tape as your primary way to splice, period. That is illegal, unsafe and will get all your work flagged by the inspector. Since you say you are in the USA, wire-nuts and splice blocks are readily available and dirt cheap, though you can solder if you really want to.
However, the solder method you want to use is not allowed inside conduit or conduit bodies, and if you do it inside a junction box, you still need to leave 6-8" of tail. Part of your wire will be a stiff stick, so it'll be hard to stuff into the box. 4-11/16 boxes will help, those are much cheaper at real electrical supply.
Also, as far as taping after the solder -- that is not an afterthought. It is complicated! Electrical-grade soldering is serious business, and not least is the fairly complicated taping of insulation, that involves both friction tape and electrical tape. You'd need to find an olllld timer that worked on K&T to educate you.
Shrink wrap might be a viable approach, but watch out for sharp points that wear and puncture the shrink wrap. Part of the friction tape's job is to remove all possibility of that.
In any case I wouldn't depend too much on NASA guidance in that most of their vehicles are single use. I would wire the way NASA's facilities department wires their boring old office buildings. Call them up, they'd be gobsmacked that anyone cares about what they do.
That is not to say there's never a reason to use tape. If you solder, it's an i,portant part of splicing, and you must do hots and neutrals. Some people also use tape to over-wrap wire nuts to "keep them on", but they need to get better nuts and use the right size! Older (20 year old) nuts are not nearly as good as today's. Exception: nuts capping off a single wire need to be taped or they will fall off.
Work must be neat, workmanlike and consistent within your installation. Nobody ever got fired for using black for everything. However that can make the wiring rather difficult to understand, which is why I own 10 colors of electrical tape.
By "consistent within your installation" I mean that if the previous work used colors a particular way, continue doing that if you are able. If unable, use what you have, but make it plain you are doing that.
Do not use bad tape simply to get a color. By "bad" I mean low quality or tape which is not UL/CSA listed for use as electrical tape.
Best Answer
It's a data cable.
Probably CAT5 or CAT5E grade. (it will be written on the blue jacket every metre.)
These cables are used for ethernet (between computers and routers) and for connecting telephones, and home automation equipment, intercoms, thermostats etc. I'm guessing there used to be a phone jack there.