So what factors would make NASA/JPL think they would find any Trojans at the Lagrange points?
The one known Earth Trojan was discovered because it got so close to the "camera"!
If a telescope could be moved across a larger area, the chances of finding another only increase.
The idea that Trojan asteroids are supposed to be at the Lagrangian points is not really right though. If you watch the Scott Manley video Asteroids In Resonance With Jupiter after
00:34 there's a nice illustration of how Trojan asteroids circulate around the Lagrange points in elongated (and sometimes teardrop-shaped) orbits.
Tadpole and horseshoe resonant orbits in a Sun-planet system, shown in a frame rotating with the planet's orbit (source: Nature)
above: image and caption borrowed from this answer. Click for larger view.
Remember that these asteroids are in heliocentric orbits. They are already in orbit around the Sun with a period of almost exactly the same as Earths. The Earth only gives tiny nudges and pulls whenever the asteroid gets closer to it, and that may happen with a period of tens or hundreds of years. So it's better to think of Trojan asteroids as "loosely associated" with the L4 and L5 Lagrangian points, and not really "held" there.
While Jupiter's pull may be substantial, it moves around in its own orbit fairly fast. So while it may pull in one direction for a few years, a half-dozen years it's pulling in the opposite direction, and so despite the strength, it is not as destabilizing as one might think at first. Remember the asteroid is in an orbit around the Sun, not the Earth.
And of course another reason that NASA/JPL thinks that there might be find-able Trojan asteroids associated with the Earth's Lagrangian points is that we definitely have at least one already!
2010 TK7 was spotted from Earth as it wound its way around it's very long Trojan orbit and got fairly close to Earth in 2010. In 2011 the paper in Nature suggests the stability could be 10,000 years. Since that time many more observations have been made and stability predictions of the orbits have been refined.
There is a nice summary of the situation in this oldie-but-goodie answer, and here is one of several slightly confusing videos of TK7's orbit. Also one can read more about Osiris REX's search as well as 2010 TK7 in: