Notice that the chair('this is the chair') where Briggs hid the clue is facing the dinner table.  This connects with the message 'the conversation at the dinner table is lively'.  There were two different messages about this dinner table, one sent by Mr. C and one received by Diane(which was capitalized and had a comma).  Following receipt of the message, Diane looks first perplexed, then contemplative; and she then ends her obscenities and breaking the rules(cursing and smoking inside the morgue) and smokes outside where she is then able to encounter a 'dinner table conversation' with Cole, rediscovering a sort of fraternity with that FBI community of people, remembering better times, etc.

How to make sense of this connection?  Briggs is trying to come back after 'hibernation'(like 'sleepwalking' and the sleeping giant) and his head is disconnected, which Hasting called beautiful, but each time he is thwarted by those he is hiding from(BOB/Mr. C, et al), just as Cooper was thwarted from returning by billionaire surveillance in New York and his potential hosts were killed as suspect.  Briggs wants to come back from sleep(the sleeper must awaken), from the red room/lodges to try again at maintaining a new law/reality/community(conversation around the dinner table).  These attempts are thwarted by the ongoing terror of Mr. C et al who are looking for coordinates and killing him again and again as soon as someone figures out how to bring him back(he has been killed 18 times or so), powerful forces (billionaires, Mr. C, etc.) are all making sure good Cooper and Briggs stay sleeping, something like killing academics here, regulating thought/spirit. Why? So Mr. C can maintain his dinner table, mafia state control/terror to allow profits/enjoyments to flow in excess, make sure the 'Laura problem' will never be solved, the trauma it exposed will never lead to confrontation and solving of the problem.  Mr. C's table is the prostitutes table at the Roadhouse, among other connected parts of the episode. For example, the goofy cops that think pain is funny(losing money on the car light, Australian with pliers etc.) and engage in obscenity almost corrupt Dougie/cooper(flag to woman scene) who follows everything he sees.  Now contrast them to serious twin peaks cops who are now able to search for red room to be able to sit in 'the' chair and see the dinner table converation/community proper.