early 15c., "complete" (implied in searchingly), present-participle adjective from search (v.). The sense of "engaged in seeking," hence also "keen, penetrating" (of gazes, etc.) is by 1570s.
Entries linking to searching
search v.
c. 1300, serchen, "go through and examine carefully and in detail" (transitive), from Old French cerchier "to search" (12c., Modern French chercher), from Latin circare "go about, wander, traverse," in Late Latin "to wander hither and thither, go round, explore," from circus "circle" (see circus). Compare Spanish cognate cercar "encircle, surround."
The meaning "make an examination of" a person, bags, etc., is from early 15c. Phrase search me as a verbal shrug of ignorance is recorded by 1901. Search engine attested from 1988. The phrase search-and-destroy as a modifier is by 1966, American English, a coinage from the Vietnam War. Search-and-rescue is by 1944.