On first glance, this poem appears to be a straightforward account of a relationship between a father and son which is strained (at best) but somehow comes together in the end over a short story written by the son.
Make no mistake. There is a lot more going on here than this. In order to understand how the ellipses tie back to the theme of the poem, you first need to define a theme which they might relate to. Look again at the very first three lines of the poem:
16 years old
during the depression
I’d come home drunk
The first thing these lines reveal is that the speaker is looking back on his teenage years, likely as an adult, which were obviously hard times (both economically and personally). "I'd come home drunk," however, is the clue to the ellipses.
The following stanzas suggest that the speaker's memory of these times are clouded by his drunken state. When his mother speaks, her voice trails into ellipses. The speaker responds, and his words trail to ellipses. Not only could the trailing off suggested the slowed down and slurred speech of drunkenness, but could also suggest a hazy memory of something that obviously happened more than once. The ellipses suggest that this account is a meshing together of what could have been several instances of a similar circumstance.
It is clear that the speaker is apathetic toward this father whom he clearly has a bad relationship with. It is suggested that the father is both emotionally and physically abusive, and the speaker has resorted to drinking in order to cope. The ellipses heighten the speaker's apathy.
Finally, at the end of the poem, the one story that the father claims to like is riddled with perverse sexual undertones.
the story held
meaning for him
when I had written it
I had no idea
of what I was
These lines suggest that the father relates to the man in the story, perhaps because his son has written about him. Also, these lines suggest, again, that the speaker could have even been drunk when he wrote the story.
With all of this in mind, I think one theme that tends to stick out here is one of escape and coping. Clearly, the speaker is dealing with an abusive father to whom he cannot relate. He uses alcohol and writing to escape this relationship and its abuse. The elipses at the beginning of the poem help set the tone of apathy and even create in the poem a mode of escape, almost to suggest that the speaker could not care less about the one and only time he and his father found a connection.