The
elves did search for
Turgon and so many of their "lost" kin. Not finding them they hoped Turgon and his followers would reappear when the need was greatest. Afterall, Turgon wasn't the first of the
Noldor to go off to build a hidden kingdom (
Doriath,
Nargothrond).
But
Gondolin so well hidden, whose entrances were guarded by the
eagles of
Manwe was never found (not counting
Húrin and Huor who were brought there blindfolded) until
Tuor under
Ulmo's protection came to the Hidden Kingdom.
Unfinished Tales, (I) Of Tuor And His Coming to Gondolin