Learn English – What’s the term for flickering eye movement

I absolutely loved this question. Of course, we can all think of a handful of words like thingy, that simply act as a stand-in word for the word we are thinking of but cannot, at present, grasp.

The 1960 Dictionary of American slang uses the term kadigin for placeholder words, defining it as a synonym for thingamajig.

Dr. Richard Nordquist, Professor Emeritus of English, writes in Crossing Boundaries: Studies in English Language, Literature, and Culture in a Global Environment, originally published in 2009:

The linguistic term for such peculiar sounding words as "thingamajig" and "whatchamacallit" is placeholder, or, less formally, tongue-tipper or kadigin: a word used to signal that a speaker does not know or cannot remember a more precise word for something.

William Safire, author, presidential speechwriter, and writer of The New York Time's column "On Language" addresses popular etymology in his incredibly popular, and entertaining, column. The focus of his January 9, 2005 piece, "Whosit's Whatchamacallit" is all about your topic:

"We are now into the creative world of "tongue-tippers," terms used in place of words on the tip of the speaker's tongue but just beyond linguistic reach."

In the article, Safire provides fascinating history and etymology of various tongue-tippers. We also learn that English may not be able to lay claim to all tounge-tippers:

"British English also has its words for the unremembered objects. In 1962, The Sunday Times explained that "'ujah' . . . was used as widely and as indiscriminately as 'gimmick' and 'gadget' are used now." It was usually spelled oojah and was thought to be of Hindustani origin."

I hope you enjoy reading the entirety of Safire's column. Between placeholder, kadigin and tongue-tipper, the last one in my opinion is the best. I think that it's important to have a memorable word when trying to remember the name for the group of words that we use when we just can't seem to remember the actual word.

Consider using Transversal or Sagittal. As you pointed out it is hard to describe such a concept because the position you want to describe is extra-relatal from the observer unlike common directional words we use. North and South are close but they are not usually imagined from the first person point of view are are un-conviently pointed to a fixed spot on the horizon in this case. Since you mentioned a third term to coalesce with horizontal and vertical the answer will be a bit subjective because the way the distances and movement between points can be described are similar in both the sagittal and transverse planes. What you are describing is comparing two points along the intersection of the horizontal and vertical planes or more likely between the sagittal and transverse planes.

In this case consider using Transversal. The intersection of the vertical plane with the horizontal plane would form a transverse. This medical definition from thefreedictionary.com describes:

transverse plane of space, n an imaginary plane that cuts the body in two, separating the superior half from the inferior half, and that lies at a right angle from the body's vertical axis.

And the definition for sagital:

sagittal plane

n.

A longitudinal plane that divides the body of a bilaterally symmetrical animal into right and left sections.

Since forward and backward movement at the intersection of the vertical planes is what you are describing, transverse or transversal may be a better choice, however when we describe vertical it is ambiguous whether we are describing a sagittal plane or a coronal

Because of this it is still necessary to describe the relative position between the points. You can use biological or aeronautical terms to describe forward and backward through the transverse plane: dorsal/posterior or aft for back and ventral/anterior and fore for forward.

Edit

After reading some of the other answers it seems clear to me that you are stuck with either a frame of reference to the earth or from the point of view of self. Perhaps the answer here is to abandon the term vertical and horizontal and use for coronal, sagittal, and transversal although that still does not solve your earth point of view in which case you can use latitude, longitude, and altitude.

But keep in mind it's all relative. Pick a system and stay consistent.