Video of lights changing:
Step 1: Controlling the lights
The programming is fairly simple, cycling between blinking the hand, holding the hand signal high (actually flashing at 50 Hz), and then holding the walk signal high.
Step 2: Wiring the Lights
The white LEDs are wired together in strings of 6, with the exception of the right thigh of the walker which has 7. I took the shortcut of wiring them together rather than putting in a different value resistor and splitting them up, but when the batteries lose voltage, this string tends to disappear.
The red LEDs are wired across the hand rather than along the border to allow for their close proximity.
The power supply for the lights consists of two 9V batteries connected in series. Each set of LEDs is connected to a transistor which receives the signal from the Arduino.