I don't think it is gold. It's just mild steel. Not worth anything I'm afraid.
The sad truth is that mechanical watches were never much good compared to modern quartz or radio watches. I have my grandfather's fob watch, which is good quality, highly decorative, has a 'fusee' or chain mechanism, and after careful cleaning and maintenance is struggling to keep within 30 seconds a day. It is very beautiful, but as a timepiece it's crap! I use a cheapo £20 John Lewis quartz wristwatch and it gains about a second a month!
I have noticed that increasingly, young people don't bother with watches at all. They use their mobiles which I assume are spot on, or can be if they take their time from GPS.