Hello.
It was hard to understand but then I got it.
What you want is a circuit which will turn on the led for a maximum time of "1 second" while the switch is pressed and turn it off when it's released.
The circuit is very very simple, it can be made with what's called as passive derivator.
What are your requirements? Does it have to glow constantly or not?
The circuit is very simple (as shown before). As you are driving a LED and this circuits generates negative spikes, add a protection diode in anti-parallel with the LED (they should point in opposite directions). The resistor is the same you want at the maximum current, then it will decrease. The capacitor value depends of the time and the resistor.
It's almost fully charged when 5.R.C [seconds] happened, so if you drive the circuit at 5V and LED voltage is about 2V, and in 1.R.C the capacitor is charged at its 66% (leaving less than 1.33V to the LED) then your forumla is:
t=R.C --> You know the time and R, calculate C.
If you don't get the calculated time, play with the values till you get a reasonable one.
If it has to glow constantly, use a comparator or some transistors with zener diodes to "digitize" the voltage applied to the LED.
That's the easiest way I know, hope it's useful for you.