While some people swear by Windex as a thinner for Tamiya acrylics, I won't use it. Whilst Windex contains an amount of alcohol, which is an effective thinner for Tamiya acrylics, it also contains some ammonia, which is very effective at breaking down the binders in the paint which make it adhere to the surface being painted. Many people use Windex to clean their airbrushes specifically for its ability to break down acrylic paint.
The best thinner for Tamiya acrylic is Tamiya's own thinner. However, if unavailable, the best alternative is (90% or better) Isopropyl alcohol. The next best option is ethanol (aka denatured alcohol or methylated spirits in some localities).
Both of these options can be somewhat problematic when airbrushing due to the fast evaporation of the alcohol. This can sometimes cause a grainy, powdery finish due to paint drying in the air between the airbrush and the surface of the model being painted. This can be reduced by airbrushing closer to the surface of the model and by adding an acrylic retarder (available from art supply stores) to your paint mix (pre-mix a few drops of retarder with your chosen thinner before mixing with your paint). Typically, I spray from 15cm or less.
Whilst I haven't had any problems using ethanol as a thinner, Ross (Triarius) has indicated that there may be some compatibility issues with certain colours in the range, so I'd suggest testing with small amounts first.