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