I'm looking for that black cloth electrical tape with very strong adhesive that's used in electronics sometimes. Like keeping antenna wires from wiggling in laptops and such.
What's the right keywords to search. Black tape just brings up the pvc variant electricians use.
That's what I searched for and I got some form of fuzzy cloth tape used to tape cable looms in cars , fuzzy to keep down rattling I guess.
The tape I'm looking for is kind of shiny and smooth.
Your description is not enough to conclusively identify it (but that isn’t a criticism of you: it can be impossible to identify an unknown tape). There are too many tapes that are visually identical but have subtly or radically different characteristics.
I think a better question is “what features are you looking for in a tape?” As in, what are the performance characteristics you require? What is the problem you’re looking to solve?
Take a look at
https://multimedia.3m.com/mws/media/371333O/specialty-catalog-05-tapes.pdf?&fn=Spec-Cat-05_Tapes.pdf — there are many cloth or filament-reinforced tapes made for electrical use. (Look at page 150.)
Hi ulwur,
something like this:
https://heinrich-haeusler.de/article-detail/1000847912
?
In germany they go unter the name "Isolierband",
may search for "PVC/Vinyl Iso-tape" or so.....
Good luck
Ach Mensch… did you even read the original post? PVC electrical tape is what OP
does not want.
Good Morning Ulwur, Back in the day, (1950s), we called it 'Friction Tape'. And I see it is still available.
Good Morning Ulwur, Back in the day, (1950s), we called it 'Friction Tape'. And I see it is still available. 
I like friction tape, but it does not have a very sticky adhesive.
I have seen the black fiber reinforced tape that the OP is referring to, but I have no idea what it is called or where to get it. It is incredibly difficult to remove from itself and other surfaces. I always end up cutting it to get it off.
The cloth tape used on automotive wiring looms is commonly called "Tesa tape", since Tesa is a leading brand name of this type of tape.
Digikey > Product Index > Tapes, Adhesives, Materials > Tape
+ filter for fabric carriers = 500 something results
I like friction tape, but it does not have a very sticky adhesive.
as above
There are too many tapes that are visually identical but have subtly or radically different characteristics.
"friction tape" as a range that as DigiKey serves up has a spread of matching styles including branding like "StrongHold". Adhesion in production relies on cleanliness/surface prep and/or activators.
I'm looking for that black cloth electrical tape with very strong adhesive that's used in electronics sometimes. Like keeping antenna wires from wiggling in laptops and such.
What's the right keywords to search. Black tape just brings up the pvc variant electricians use.
In the tape you're thinking of, is the cloth more like cotton cloth, or more like a shiny, woven synthetic ribbon?
In the tape you're thinking of, is the cloth more like cotton cloth, or more like a shiny, woven synthetic ribbon?
The tape I remember was shiny black with visible fiber reinforcement, relatively thin, and not very stretchy. I think it came in all colors.
The tape I remember was shiny black with visible fiber reinforcement, relatively thin, and not very stretchy.
almost sounds like gaffer tape
Try searching for
acid tape or acetic acid tape
The tape I remember was shiny black with visible fiber reinforcement, relatively thin, and not very stretchy.
almost sounds like gaffer tape
Gaffer's tape is one of the thickest tapes you can get.

So it definitely doesn't meet the "relatively thin" descriptor.
Try searching for
acid tape or acetic acid tape
Are those poor translations of "acetate tape"? It certainly looks like acetate cloth tape might be what OP is looking for.
(Acetate ≠ acid ≠ acetic acid. They're not the same thing, even if acetate is made from acetic acid.)
Gaffer's tape is one of the thickest tapes you can get.
not if yer buying the cheap stuff
Gaffer's tape is one of the thickest tapes you can get.
not if yer buying the cheap stuff
I've never seen gaffer's tape that even remotely qualifies as "thin".