The LSL, Auto Train, and EB all require 2 engines simply due to the fact of how many cars they are hauling. Without a second engine, acceleration from a stop would be very poor and would gradually snow ball into a late train. Any other Amtrak train crossing mountains also needs a second engine in order to make the climb at a reasonable rate of speed; that would include the Capitol, Zephyr, Starlight, & SW Chief. The Sunset is probably borderline, so it generally gets a second engine.
But that leaves the Crescent, Silvers, City, and the Eagle all of which could run with one engine. As other's have noted, the wisdom of doing so is very debatable, especially considering the failure rate of the P42's. And in fact, because of that failure rate, CSX now requires Amtrak to always have 2 locos on all LD's that run on CSX tracks. That "agreement" has been in effect now for about 3 or 4 years IIRC.