Firstly, learn to tell the billies from the nannies. The billy horns are pretty well an even arc over the entire length of the horn. The nanny horns go quite straight, then make a sharper turn near the end.
The oldest billies tend to either get tired of staying with the herd, or else are kicked out. Look for a lone goat, often at lower altitued than normal, and the color may not appear a nice white. Such an animal is likely the oldest billy on the hill!