Nice stove! 

I can't offer anything about the button colors or how they worked, but there are probably pictures either in the archived posts here, or elsewhere on the web, or a member may have some literature or the knowledge about them to advise you.  I would hazard a guess that they go from green for "LO" then into yellow and orange, then red for the "HI" button.

Is the minute timer mechanical or does it have an electric motor?  I may be a combination, with mechanical timer mechanism that triggers an electric buzzer of some kind.  If it's mechanical, it probably just needs cleaning and or lubing with clock oil.

I can say with a good degree of certainty that your stove's clock was made by Telechron, a clock company that GE owned when your stove was manufactured.  The likely reason it's not running is because the rotor is gummed up and/or needs oil.  Telechron was a little skimpy with their application of oil.   These rotors were used on all types of GE and Telechron clocks (and a number of other makes) from roughly 1940 until around 1970, but replacements are no longer made.   They can be expensive on ebay, but there's an easy way to revive one.  Unplug the stove's power cord before performing any work.

I'm providing pictures of a type H3 (3.6 RPM) rotor along with pictures of one installed in its coil assembly.  Some have steel housings, others have copper ones.   They're interchangeable as long as the 3.6 RPM specs are the same (stamped on the side of the rotor housing). 

When you access the clock from the rear, you'll see what resembles the assembly pictured below.  If you can extract the rotor without removing the entire clock, fine.  Loosen the screws and swing out the two flat L-shaped sections of the field coil that hold the rotor in place.   If there are spacers surrounding the screws, be ready to catch them.  The coil sections may be a little stiff or sticky, but they'll rotate out of the way and allow you to extract the rotor, which lifts right out.  Be very careful not to disturb the paper wrapped field coil where the 110V wires connect.  These were fragile when new, and are even more so now.   I assume your clock mechanism may include a timer of some kind, so there may be little flaps and doo-dads not shown in the picture below.  Try not to disturb those either.

With the rotor out, find yourself a lamp with a 60 to 100 watt incandescent bulb that is situated vertically, and a can of 3-in-1 Oil with the blue and white label.  Carefully balance the small end of the rotor on top of the bulb, with pinion gear side aimed up.  Turn on the lamp and let the rotor cook for about half an hour.  Turn off the lamp and place a drop or two of oil on the side of the pinion gear so it fills the small well at the bottom of the gear.  As the bulb cools, it should suck the oil in.  Repeat this as the well empties until you've added no more than 15 drops.  Too much oil will bog down the rotor and cause the clock to run slow.  If the rotor stops accepting the oil before you've hit 15 drops, you may need to re-heat and pick up where you left off,  adding only the remaining number of drops to reach 15.  Soak up any oil that might be on the gear or remain in the well.

The rotor will be hot to the touch.  Either let it cool, or insulate your fingers with a rag or paper towel, and place it back into the clock.   Make sure it's properly positioned so the pinion gear meshes with its corresponding gear in the clock movement.   Move the field coil sections back into place to secure the rotor, and tighten the screws -- not too tight, not too loose.   Reconnect the power cord and check the second hand for sweep action.  If there's no movement, the rotor may be shot, but that would be kind of rare.  You could try cooking it again, but I wouldn't add any more oil.  If that doesn't help, you'll need to do surgery, but let's not cross that bridge until we come to it.