This article is from the Toyota Tundra FAQ, by Steve Yee with numerous contributions by others.
There has been some discussions on TundraSolutions and Usenet as to what is
causing this tapping sound that usually comes after starting the engine.
As of June of 2001, the culprit finally has been found ! In many cases, the
exhaust manifold has cracked slightly. The gap then allows a tapping noise to
escape, and in most situations, will disappear when the engine is hot due to
metal expansion sealing the crack.