Thanks for your response.
I'm familiar with that portion of the rules. However, that deals with constant effects, which is not the effect of Bilbo's ring. The ring doesn't keep Bilbo invisible forever once it's activated. Rather, it turns him invisible or not based on whether he has the ring on or not - clearly a concentration-based effect (as evidenced by the rules using an invisibility ring by way of example in the section on concentration duration for magic items).
I understand that if the ring were made a constant effect it would avoid flicker. But that doesn't really meet the parameters of the item in question.
See a contrasting view on "constant" effects here. This discussion determined that "constant" effects were one-and-done effects that were not renewed each sunrise/sunset, but rather were cast once and then maintained forever. Curiously, they too had a quote from David Chart to support their interpretation.
I note as well that even under the interpretation made in your link (i.e., that the invisibility effect would end if Biblo were not in contact with the ring at sunrise/sunset), that still isn't quite an invisibility ring a la the Hobbit et al. According to that interpretation the ring would make you invisible regardless of whether you took it off until sunrise/sunset. I'm wondering if it's possible to emulate a ring that turns you invisible when it's worn, but turns you visible when you take it off, all without flicker. A tall order, perhaps.