[Mümmel]

Picture part 2):

The above circuit shows the gear lights driving circuit and the connection to the gear lever switch.
In shown position, the gear switch output is low. This should correspond to gear up position.
The three upper LED’s and the red LED are dark.
When the gear switch is flipped to gear down position, the upper one-shot gets triggered, and produces a positive pulse of about 4.7seconds at the Q output. (determined by R*C of the upper one shot timing components) This pulse drives the lower transistor and the red LED will light for 4.7 seconds. At the same time, Q of the upper one-shot produces a low (going to 0V) pulse of 4.7 seconds. This pulse will pull down the base of the transistor that drives the three gear down LED’s.
After 4.7 seconds, Q goes low, and Q goes high. The red light goes out, and the green lights light-up driven by the high output of the gear switch.

When the gear lever is again pushed in the gear up position, the switch output goes low, and the green lights go out. At the same time, the lower one-shot is triggered, and its Q output sends a high pulse of 4.7seconds to the red LED driver transistor.

You can change the gear transition time by changing the 470k resistor value or the 10uF capacitor value of upper and lower one shots: Upper determines up à down time, lower determines the downà up time.