I need help designing a very simple timer
This is a very simple thing to do for a small microcontroller.  Even the smallest of them all, the PIC 10F200 can easily to this job.  It has a internal oscillator that is well within your accuracy requirements.  Otherwise, it only has to control 2 outputs, which is fine since it has 3.

A nice thing about a micro is that you can customize things a bit.  For example, you might realize after a while that you don't always notice when the light turns color.  It would be easy to have the micro flash the new state at 2 Hz for the first 5 seconds or something.