It's not "Taps." It's "Il Silenzio," a trumpet piece written by Nini Rosso in 1965. It bears a superficial resemblance to "Taps" and is inspired by the Italian bugle call used in a similar way. I repeat: It is not "Taps." There is no "long version" of that call. What you hear at lights-out and at military funerals IS the full version.
This is Il Silencio, it's not taps. It sounds like taps, but it's more akin to a russian calvalry call. It's also the song played at the end of American Sniper.
@wizardzofid I have no idea I'm sorry. The video is flagged as having matched third party content so there must be other uploads which may contain more information.