Enamel thinner and Tamiya acrylic don't mix well. the acrylic could turn into little globs inside your airbrush. (not thinking one day I put enamel thinner instead of acrylic thinner into a mixing jar with acrylics. It wasn't pretty! )
Lacquer thinner would work to clean it though, although the fumes of lacquer thinner are rather toxic if breathed into your lungs. Myself, I save lacquer thinner for lacquer paints and cleaning the airbrush for it's monthly overhaul, when spraying acrylics windex is strong enough to clean between colors and at the end of the night. For regular brushes soapy water, water or windex would clean the acrylic, but lacquer thinner is capable of cleaning it off too.
With an all metal airbrush nothing should hurt it as far as solvents. The only thing solvents can hurt on it are the rubber O-rings where the plunger is at the top of the airvalve assembly. That part of the brush should never be soaked in a solvent unless you first take out the air valve with the O-rings on it. Typically major maintenance on the airbrush should be done once every couple of weeks, and all that usually needs to be soaked in a solvent, is the head and tip of the brush. Everything else can be wiped down to remove any dried on paint if needed, but that's about it.