My beloved wife has been heard to say something like: “To wrap this gift, you’ll need scotch tape and a scissor.”
IMHO, scissors (like pants and shorts) doesn’t exist as a singular. It’s always plural. it’s either “get me the scissors” or “use a pair of scissors”. I thought she was the only one in existence until last night when we saw an old episode of Curb Your Enthusiasm, and Larry David used the singular. Anybody else?
My Midwestern MIL, of beloved memory, was known to say it that way on occasion, but not always. She grew up in a small town in south central Iowa.
Deep cut, but Bert says “a scissor” in the gift exchange/gift opening scene in Christmas Eve on Sesame Street. Frank Oz (Bert) is Jewish-Belgian-Californian.
I had a pair of kitchen shears that came apart for easy cleaning (absolutely necessary for spatch-cocking a chicken). My daughter once picked one side up from the dish drainage area and asked me what the heck it was. I told her it was a scissor, then I picked up the other half, put it together, and said, now it is scissors…
I suppose that makes sense. I mean, one half of a pair of pants is a “pant leg,” not “pants leg.”
Often, a tool or device consisting of two parts connected by a hinge or pivot gets a name of the form “pair of Xs” or just “Xs” for short. Over time the singular tends to replace plural usage. The compass (tool for drawing circles) used to be called “a pair of compasses.” The nutcracker used to be “a pair of nutcrackers.” Likewise pincer and stepladder. In the case of tweezers and tongs and scissors, the plural is still ahead but the singular seems to be catching up.
Allan Sherman: “What is half a pair of scissors, but a single sciz?”
My grandmother, who grew up and lived in SW Ohio, would say scissor.
Scissor is singular in German, and I know there were once a lot of German speakers in that area.
You can use a scissor when making certain articles of clothing, like a trouser, jean or pant. A tweezer and plier can also be useful.
In spanish that process is not yet complete for pincers, sometimes we say “pasame la pinza” (get me the pincer) and sometimes we say “pasame las pinzas” (get me the pincerS), and both times we mean the same thing.
The clothing industry is now using the word “pant” for a single pair of pants.
Some martial arts have a move called a scissor kick. The term can also be a synonym for a bicycle kick in soccer.
Spoken language often decides to drop uneeded sounds. In a similar way pants are evolving to a usage of pant.
Ninjaed while I searched.
The singular tool known as a pair of pliers, often just called pliers, is two pliers, or levers, connected together. Rarely is a prying device like a crowbar called a plier though. Small airplanes often have pants covering exposed wheels to make them more streamlined. Although referred to collectively as pants most often there is an individual pant on 2 or 3 different wheels. Language is subject to entropic effects.
Scissor lift – two words or adjective and noun or jury’s still out? 
I vote adjective. ‘Lift scissor’ reverses the word order and their grammatical form, and illustrates an accepted form of a singular scissor.
Half of a pair of scissors is a blade, damn it 
Singular scissor = pair of scissors is obsolete, according to the dictionary.
The padded mats we got from one of our suppliers at work gives handy tips on how to inspect selected medical instruments, such as the Mayo scissor and the Adson forcep. Furthermore, we used to have carts of instruments with drawers labeled SCISSOR’S and FORCEP’S: whether that qualifies or not is up to you.
I honestly try to take a descriptivist point of view on word usage, but it’s hard sometimes.
I don’t think using ‘scissor’ to refer to a mechanism that employs a combination of scissoring members is off base as in the example I cite of a ‘lift scissor’. If someone says “This cardboard is hard to cut straight with a knife” and a response was offered “Use a scissor instead” it could be understood to mean the mechanism consisting of a pair of knives, although it sounds quite clumsy.
Latest quote in my OED is from 1611. It sounds clumsy because few people today say it. Does not mean it is automatically wrong or off base.
Scissor (verb) is still in current use.
I’ll bet they also call a single biceps muscle a “bicep.”