Is there a term for this piece of hair?

So I usually look at this part and my side burns to tell if I need a hair cut. The part I refer to is probably the start of a pony tail (I'm a guy btw). This is only on the back of the head, but not all people get this. Here is an image that shows what I'm referring to.

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Clearly at the bottom of his hair, there is a small pony tail-like hair piece. Is there a term for this?

A rat-tail or rattail is the term for a small, thin piece of hair protruding from the base of otherwise short hair. These are often braided and can be quite long, but they aren't always. See here for some examples of short, unbraided styles still deemed rat-tails (as well examples of their longer and braided cousins).

The expression tapered nape area seems to fit. The nape (the back of the neck) hairline is different for everyone of us. In the OP's case his nape hairline tapers towards the centre creating a mini-ponytail.

There are three basic styles of rear hairline: Block, round, and tapered.

Here is a woman's hairstyle seen from behind, where the nape hairline is deliberately cut into a triangular shape

Napes (predominantly super-short) are neatly outlined to follow the natural contours of the hairline, beneath either distinctive “weight-lines” of the blunt cut bob, or graduated/ tapered into the soft, feminine curve of the lower neck.
Source: Hair Xstatic

Different types of nape hairlines

Nape hairline. This is the hairline at the back of the neck. Care is needed particularly when designing shorter styles because this hairline can grow into a point at the centre of the nape, or into two points, or into three, or sometimes can grow straight across the nape.

Source: Hairdressing world.com

Image of a boy's nape hairline which has a natural point in the centre.

I'd call it a prospective/potential/upcoming pig-tail.

• prospective - "likely to be or become something specified in the future"

• potential - "capable of becoming real"

• upcoming - "happening or appearing soon"