TER: Any advantage to booking in advance?

You are correct about the price. These are also tickets that you have to pick up at the station. For me the process of retrieving the ticket at the station is easier than buying the ticket. I usually retrieve all my tickets at the first station that I use during a trip. Others prefer to retrieve them just prior to each trip to reduce the risk of loss.

Thanks again, JHK.

(I've bought most of my train tickets already, but this is one case in which there's some value to us in being flexible about departure time. We don't know when we'll want to leave, exactly. So, we'll wing it, since there's no prepurchase discount.)

I've done this, actually with a continuation on to Geneva. You can just buy tickets at the station. We bought in advance, but could not retrieve them from the machine, as the credit card we bought with did not have a chip (at that time), then the first ticket agent could not retrieve because her terminal had a broken magnetic strip reader. That is not unusual, since only Americans carry these antiquated cards. Fortunately, the other agent's terminal could read our card and we got our tickets.