Neon lamp symbol

Neon lamps are not polarised but only the more negative electrode will light up.

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Figure 1. Only the cathode lights up. +DC (left), -DC (center), AC (right) supplied to NE-2 type neon lamps. Source: Wikipedia Neon lamp.

For an AC supply the anode and cathode swap on each half-cycle of the AC supply so connection polarity doesn't matter.

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Figure 2. NE-2 type neon lamp powered by alternating current (AC). Source: Wikipedia.

The linked article may explain more.

Where do I place the dot, then? At the center or at one extreme?

Either location of the dot should convey the meaning that it is a gas-filled lamp.

The dot denotes a gas-filled tube, which distinguishes it from a normal vacuum tube. Neon bulbs and voltage regulator tubes1, as well as certain types of high-power tubes such as thyratrons and mercury-vapor rectifiers fall into this category.

The neon bulb is not polarized; it is symmetrical.

1 See also Anyone recognise this capacitor and its symbol (circle with dot)?

A neon lamp is not polarised. It may be connected either way.

The dot signifies that it's a gas-filled lamp.