^^^ one of his books ^^^

The idea is that by carrying their ideas forward, you honor your departed friends in a more profound way than you would by just saying a few kind words at their funeral. By the way, I searched the text to find more context and found that it seems to be two different plagiarized passages cobbled together. The first part is from an essay by Hua Hsu that was in The New Yorker, and the second part is from a review of one of Hua Hsu's book by Vanessa Hua that was published on a site called Alta.

You are right to be confused by this poorly written sentence. It is not at all clear what it is that is "signaling". One possibility is that his colleague's writing is signaling. Another possibility is that "taking seriously the ideas" is signaling, although this doesn't make sense because "taking seriously" doesn't signal anything. In the latter case, "signaling" is simply the wrong word. A better word would be "suggesting". Another problem is that neither "leaving him alone" nor "abandoning him" makes sense in the context of a eulogy.

They want to best honor their friend that died at their funeral by giving a speech (eulogy) that is only about the friend. This friends death communicates (signals) the chance or hope or (possibility) that the funeral speech (eulogy) is about the dead friend and not about you or how much you miss them. I hope that helps....