The gumshoe is an unobtainable vehicle in GTA Chinatown Wars. Don't ask how to obtain it, because it's impossible. It only shows up during the mission Scrambled for Wade Heston. The vehicle may also show up for a brief moment in the mission Sources for Chan Jaoming, an exclusive mission only for the PSP.
It IS obtainable, but not in the normal game. You have to use some cheats for the PSP version. All I know is the default radio in is is Alchemist.