TS 555 timer with trigger network

I wanted to pimp my son's bobby car by installing a few lights, they should go on for a few minutes once he starts moving the car. I've installed a few LEDs and a micro switch attached to the rear axle for this. So that the microswitch will get triggered from time to time.

Connecting LEDs was quite simple, but I had some difficulties building a circuit that would enable the lights for a few minutes. I've decided to use a 555 timer - plenty of examples exist of how to assemble it. I just wanted one that would be energy efficient on stand-by, and the lights should always go off after a few minutes. This was difficult because you have to trigger the 555 by short impulse, otherwise, it will never go off. My solution with micro switch has this one catch: it can remain shorted for a very long time. I could ask my son to keep pushing the car until he hears the second click..... instead, I've used a trigger network.

In the end, I had to find the right values for all components in a way that would guarantee the functionality and ensure low power consumption to not drain batteries over a few days. Actually, I did not calculate those values, I've used an oscilloscope to make sure that timing on 555 pins is right. Probably I've got not a perfect value, but on the other hand side it does what it is supposed to be doing, and it runs on a single battery for months :)

Here is the Fritzing drawing.