Okay, first, they're not dyes, which work pretty well in any suspended media. They're ions.

When you put table salt in water it breaks down into Sodium ions and Chlorine ions that attach to different parts of water molecules and float freely. The same thing happens with fuel colorants. The problem is, you need a colorant to make the ionization happen. that's why every recipe suggests alcohol: the burns, AND it's a polar solvent.

Methanol is the best for colored fuels because it doesn't have any carbon bonds to break (which gives of hot body radiation = a lot of light). Methanol flames are amongst the weakest of all and are invisible to most recording media. Plus with a molecule almost the size of water, there's a LOT of space for the ionization to happen. Unfortunately, it's also the most dangerous, turning into formic acid when introduced to the body, and having multiple entry vectors including inhalation. Please make sure to drink a beer or two after handling methanol. (ethanol elimination also clears out formic acid)

Ethanol is next best, and many people like denatured alcohol which is ethanol cut with methanol. Thing is, Ethanol has two carbons, and thus has a carbon bond to give off light. This dilutes the ionic colors a bit into pastels, typically. The double carbons also slow down the dissolving process, it takes much longer to dissolve the salts in the mix (sometimes days). People's biggest mistakes here tend to be not waiting long enough for the mix to happen.

Isopropanol has 3 carbons, two carbon bonds, much more light, much less polar. But the problems with ethanol are multiplied. It may takes months for the ions to thoroughly saturate the mix on their own, and the light from the molecule is twice as bright as ethanol (99% iso works almost exactly like white gas).

Pentane; The shortest liquid alkane and one of the primary ingredients in white gas. It has 5 carbons and no OH group, so it's entirely non-polar. Even if you could convince the ions to form, which this stuff can't do, The carbon bond issue is multiplied again: The oxidation of a carbon chain through combustion gives off a truly prodigious amount of light. So even if the ions do manage to give off their part of the spectra, it's entirely drowned in the bright white of the petrol.

Hexane, Ocatane, Nonane,, etc also in white gas, also nonpolar carbon chains, (sometimes rings) each one taking you another step away from what you want.