TS 555 Timer With Trigger Network

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

Connecting LEDs was quiet simple, but I had some difficulties to build circuit that will enable the lights for few minutes. I've decided to use 555 timer - there are plenty of examples out there how to assemble it. I just wanted one, that will be energy efficient on stand by, and the lights should always go off after few minutes. This was not so easy, 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, that it can remain shorted for very long time. I've could ask my son to keep pushing the car unless he hears the second click..... instead I've used a trigger network.

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

Here is the Fritzing drawing.