In fact, the Yerushalmi states that one's devotion to Hashem is measured by the level of his שׁמִירַת עְינַיִם. Hashem tells us "תְּנָה בְנִי לִבְּךָ לִי וְעְינֶיךָ דְּרָכַי תִּצֹּרְנָה" My son, give Me your heart; your eyes should watch My ways. (משלי כג כו) Rebbi Levi explains that the heart and eye are the two agents of sin. In this possuk, Hakadosh Baruch Hu says to every one of us: "אִי יְהַבְתְּ לִי לִבָּךְ וְעִינָךְ אֲנָא יָדַע דְּאַתְּ לִי", If you give Me your heart and eyes, I know that you are Mine.
(תלמוד ירושלמי ברכות פ"א ה"ה)
These words of Chazal reiterate how this is a most core component of our Avodas Hashem. Living a Torah life and fulfilling all the mitzvos is still not enough to prove our dedication to Hashem; we must also fully commit to guarding our eyes in order to be regarded as "belonging" to Him.
To demonstrate this idea, Reb Elazar Azkari, the Ba'al Hacharedim, offers a profound mashal. A wealthy man gifted his friend with a thousand slaves to make his friend's life easier. The friend happily accepted them and enjoyed the luxury of being served by so many. After some time passed, the wealthy man asked his friend to return only two of the servants he had given him, but the friend flatly refused. "Why," he said, "I have so much use of them, it would be such a shame to give them back!" Surely, someone with such behavior would be viewed as an ungrateful and selfish person. His actions clearly display his ingratitude towards his benefactor.
The same analogy could be applied to ourselves. We were granted two hundred and forty-eight priceless gifts from Above — our precious limbs and senses. And what does Hashem ask for in return? Just two of them, the eyes and the heart. If we are not prepared to fully commit even two of the 248 to our Creator, we are akin to the man in the story; self-centered, ungrateful and not devoted to Hashem.
This Mashal serves as a reminder that we must be willing to dedicate ourselves fully to Hashem, Who's the One that granted us all of this. Through giving up on our own selfish desires we will truly belong to Him.
(ספר חרדים, מצוות התלויות בא"י פ"ד)