Why do some people lick the tip of a pencil before trying to write with it (similarly, why did most elderly women lick their eyebrow pencil before applying)?

Possibly connected to the following, either by habit or by looking for the same outcome:

In the old days the filaments used in pencils were made of different material than today's graphite which is charcoal colored and its particles separate easily on friction with the paper surface leaving clear marks. The old material did not leave much of a mark on the paper due to its high density. It was water soluble and if left in a water filled container, would dissolve completely. On contact with water it changes color from dark charcoal like color to violet blue. In order to leave a clear mark on paper it was necessary to actually moisten the tip of the pencil filament with your saliva, the resulting product behaved and flowed like ink.

http://www.madsci.org/posts/archives/1999-11/941497627.Sh.r.html

In the old days (before I was born) pencil "leads" weren't as good as they are today. Licking them would make them mark more darkly. Last I checked--not recently--that's still the case with colored pencils.

From an old (February 9, 1994) MIT source:

A writer to the "How & Why" column in The Boston Globe asked why so many people, before putting pencil to paper, lick the tip? "Is there something about saliva that makes graphite flow better?"

For the answer, which was "yes," the Globe turned to Dr. Jack B. Howard, professor of chemical engineering, who said he himself licks his pencil tip at times.

"If the lead were truly graphite, then wetting it would probably not make a difference," said Dr. Howard, whose research includes work on graphite and other forms of carbon. But in pencil leads, he said, "the graphite is actually a mix of graphite and some clays," which are added to control the hardness of the lead.

"My observation is that wetting the pencil allows you to get a darker line," Dr. Howard said. "There's a softening of the material, some absorption of moisture into pore spaces that makes a mix that will rub off more easily. If it were pure graphite, there would be no pores to let the moisture in."

Is it a safe practice? Yes, said Dr. Howard, the graphite-clay mixture is "perfectly innocuous."

http://web.mit.edu/newsoffice/1994/here-there-0209.html

I remember being instructed in the use of an eyebrow pencil by my mother, with the first step being to moisten the pencil to ensure it applied color smoothly. While I haven't used one for many years, I would probably still start by licking it if there was no sink handy! As this link says that the tip should be clean and dry, it seems that the chemical composition of eyebrow pencils has probably changed in the last 50 years!

https://www.essentialbeauty.com.au/using-brow-powders-or-pencils-the-right-way/