[pcohoon]

Looking for advice on a solution that would be able to dissipate/hold light.

As a poor example, a solution that if contained within a tube and had a light shone from below, would resemble a ‘light-saber.’

The solution would therefore need to be translucent/have a consistent turbidity (no settling).
Furthermore, the solution must have a very low freezing point.

Hope this is coherent and not a complete load of bosh. Thank you for any advice / suggestions.

[Enthalpy]

You don't even need a liquid, do you? Because any transparent rod will lead light, for instance Pmma (fragile) or polycarbonate. Just make some transverse corrugations, say with sand paper, where you want a bit of light to escape - make a few trials to dose the distribution of corrugations along the length. You may add black paint at the end to avoid the brilliant point there.

This allows you to change the colour of your light after the sabre is built.

Light should be parallel enough when entering the rod to be fully guided and avoid a bright spot there, so use parabolic reflectors, absorbers...

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If you really want a liquid (but why?), you might consider an emulsion, as the droplets can be really tiny and stable over time, and the concentration adjusts the diffusion. Add antifreeze if you like water but need operation below 0°C. Milk is a model and an easy experimental material; switch to perennial materials later.