My 2001 Tundra V8 runs great. No check engine light. No codes. But it makes a fluttering sound. Seems to come from the left side of the engine area. Does it at idle in park, neutral , or drive. When in park or neutral and I rev it up then idle. The noise stops when revved and starts again after at idle for approx 7 seconds. Every time. Shut the truck off and restart and it may not occur immediately. Any help?

 

Is it more prevalent when the engine is cold and goes away or lessens as it warms up?

Hard to diagnose online (my wife says it has butterflies) but I'm guessing you've discovered the cracked exhaust manifold issue.....