Fade in and out 12v LED strip
Any circuit that could generate PWM of varying duty cycles would suffice.  You don't need to drive the LEDs; your circuit only needs to source a few milliamps.  You will send its output into the input of any common readily available $9  amplifier, and that will drive the lights. 

You want the PWM to be up in at least the multiple hundreds of Hz to avoid visible flicker, and it's OK to change the frequency.  The amplifier will simply follow the input.  

Also keep in mind LED strip tech is all wired "positive ground".