"deep gaze" is correct and usable in written English.
You could use it to describe the look someone is giving you, for example, "He looked at me with a deep gaze, as if he knew something I didn't."
His many biographers comment on his deep gaze.
Depardieu does what he does best as a barely domesticated beast of desire, and Truffaut's camera loves Ardant, with her quasi-martial bearing, deep gaze, and calm mystery.
DISCO turned out to be easily adaptable for the T2000 Deep Gaze smart surveillance cameras, running as a distributed computing network.
The deep gaze of the Hubble offers a view into the remote past; all telescopes are time machines of sorts, gathering light emitted long ago.
I'll never forget how deep his gaze could be with those lovely blue eyes.
But there is no time for too deep a gaze at this stage.
With every coy head nod, casual hand wave and deep eye gaze, I felt he already knew me.
Drum beats feel like stifled breaths; a near-constant, high-pitched ring and pit-of-the-stomach growl laced through the rattle of her van, as she trawls Glasgow's streets with a deep, steely gaze.
To achieve the equity we all claim to be in search of, philanthropy must have a look (no, a deep long gaze) in the mirror and have some very uncomfortable conversations about who we are, what we believe, and how we could adapt our approaches to new realities and environments where change is constant.
Joanna Hogg is an artist and film-maker who challenges her audiences with her calm, deep-focus gaze.
'We turned on one another deep, drowned gazes, and exchanged a kiss that reduced my bones to rubber and my brain to gruel.' Peter De Vries, 1954 When did we humans steal our first kiss?
