The BSA Insignia Guide, in the Boy Scout Advancement section, says "Eagle Award, silver medal suspended from scroll, ... Adults wear only on formal Eagle occasions." This would seem to imply that until the boy is 18, he can wear it for any occasion, formal or not. For adults though, the Guide specifically says "Adults wear only on formal Eagle occasions". My observation for medals in general, is that most only wear their medals for courts of honor and such. But unless the term "formal" is clearly defined, I would say that whenever the wearer feels proud enough to wear the medal, then that is a formal occasion.
The Insignia Guide is inconsistent about medals and when to wear them. For several, such as the Silver Beaver and Silver Antelope, the Guide says "formal wear". For others such as the Scoutmaster's Key, it says "key or embroidered square knot may be worn", with no mention of whether the occasion is formal or not. For religious emblems it says "Adult religious emblems are generally worn only on formal occasions." My philosphy is that as long as it is in good taste, and not specifically restricted as in the case of the Eagle medal (adults), one may wear his medals whenever desired.
Having said all this, 13EagleT430 has spent close to one third of his life working to earn his Eagle medal and should be entitled to wear it proudly for all the world to see.