The phrase "and eventually finding a" is correct and usable in written English.
It can be used when describing a process or journey that leads to a discovery or conclusion over time.
Example: "After years of searching, she was thrilled to be and eventually finding a solution to her problem."
Alternatives: "and ultimately discovering a" or "and finally locating a".
From his early success as a founding member of post-punk band PiL, alcoholism, working on the London Underground, and eventually, finding a way back into music.
Flynn, having become semi-itinerant himself, drifts from one job to another, taking in a little education, writing poetry, living on a shabby boat moored off Provincetown, and eventually finding a regular job as a worker in a homeless refuge in downtown Boston.
She told me about Emma Goldman, Ellen Knauff and Ignatz Mezei, and on Monday I caught the Miss New Jersey out of Liberty State Park to see whether I could find their ghosts at Ellis Island in the same way that, on earlier visits, I had felt the presence of my maternal grandfather, who came through in 1908 from England looking for and eventually finding a new life.
Also young men feared that their tainted sexuality would limit their chances of being with women and eventually finding a woman who would take of them.
That undiluted light will be hard to muster in the near future without a building, but the collection exists, and the goal of keeping it together and eventually finding it a new home of its own should be widely embraced.
She went to Cornwall and stayed with friends, eventually finding a small church where she could find herself again.
On the scale of DNA, finding the mutations so far away from the gene was much like looking for one's car in a parking lot, and eventually finding it in a vacant field in another town.
As a young boy, in the eighteen-thirties (a decade before Flaubert wrote that he wanted to move to Istanbul and buy a slave), he'd been brought to Istanbul and sold into slavery, eventually finding a place in the household of the governor of Tunis, where he was brought up speaking Arabic.
And so we did, eventually finding a moderate number of lizards.
On my daily runs, I'd go and look at rental properties, eventually finding a Fitzroy apartment.
Fleeing his horrified creator and eventually finding temporary sanctuary in a shack attached to a cottage, the Creature watches and listens to the elderly man and his family next door.
