Wow... that is a really simple setup for a TT.
Red and black are: ignition power and ground respectively.
White is a toss-up since it is most likely a signal wire, either RPM or TPS signal. But, may possibly be for a connection to the E-brake pedal... if it is a really simple setup with JUST a timer built in.
My HKS Type-1 TT, is tied into the RPM signal, TPS, & VSS (maybe more) and has a "smart learn" capability where based on the collected signals it makes a judgment on how long the car should stay on.