'eternal search' is correct and usable in written English.
It is used to refer to a never-ending search for something. For example, "He embarked on an eternal search for the truth."
We seem to be in an eternal search for the perfect model.
She has very narrow feet, and is on an eternal search for shoes in size 8 1/2AAA or 8 1/2AAAA.
Mr. Hier said the saga of the Exodus provides a vehicle for appreciating "the eternal search for tolerance" and, more specifically, the Jewish experience of persecution and oppression.
The playwright, once a priest, professes to be writing about the universal need for human contact and the eternal search for faith.
Even when she is on vacation in Maine, her eternal search for the sort of cork-lined room that Proust extolled is in the back of her mind.
Their partnership was one match old, and they were already giving each other lines, another benefit to Qureshi's eternal search for international partners.
If there's a theme that connects the songs on "Take It to Heart," it is the eternal pop search for true love and a spiritual center.
What it comes down to, in this place and time, is that the eternal adolescent search for self is going on at the same time as the quest for the perfect résumé.
He is an eternal nomad, searching for the right personality, the right lifestyle, the right woman, and the right country.
Set in Kinvara on the west coast of Ireland, where Thompson lives, The New Policeman makes the impossible credible in a seductive story about 15-year-old JJ, who visits the land of eternal youth, in search of Time - the perfect birthday present for his mother, whose constant lament is the shortage of it in her life.
In our age of the most profound relativism, he offers an ongoing search for eternal values, eternal truths.
