Sleep I would often share with him.
While this line initially seems to speak to a certain sexuality to the relationship, Frank later clarifies that when he told the man of his feelings, the man was charitable and sensitive about it but ultimately rejected him. So the love was a Platonic one. A Platonic love is a love or a friendship which is intimate and affectionate, but not sexual.
As a more common introductory phase of this letter, he means that they were either sleeping on the same room/bedroom, as they spent their entire days together.
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