to search out: to look through a place, a person, or a matter thoroughly in order to bring to light what is hidden
At its core this verb is about a determined, thorough search, the kind that turns a place over or hunts a person down until what is concealed is found. It is stronger than a casual look. Laban ransacks a whole camp for his stolen images, a steward opens every sack from oldest to youngest, and God vows to hunt fugitives out of the depths of the sea or the top of a mountain.
The same verb reaches inward. To search one's own heart or examine one's ways is to apply that thoroughness to oneself, and the poet pictures God's lamp searching the innermost person. Because the object can be almost anything hidden (a lost item, a fleeing enemy, buried wisdom, a secret scheme), English translators rotate among search, search out, seek, and ransack depending on what is being looked for.
What holds these uses together is the act of ferreting out what is not on the surface. When the thing sought is good, it is diligent pursuit; when it is a person in flight, it is a manhunt; when it is a plot, it shades into devising.