Kitchen timer to light up LED while counting

First what I want:

push button (first time)
LED lights up
kitchen timer starts counting up

push button (second time)
LED turns off
Timer stops

Basically just adding an LED to a kitchen timer to turn on/off with the count up timer function. The LED circuit could turn on the timer (momentary switch) if that would be easier. If anyone can help me with this it would be appreciated.