Long post coming up! I'm just going to describe the photos with a few remarks, before some notes on how the Bodensee S-Bahn operates. Until I get a masterpost up, if you've missed the Bodensee round trip, here's the final post and there are links to work backwards from there.
Allensbach, Germany. SBB Seehas RABe 521 FLIRT on a S6 local service between Engen and Konstanz.
Radolfzell, Germany. DB Regio BR 650 RegioShuttle Diesel railcar about to depart at sunset on a S61 local service to Stockach.
Überlingen, Germany. DB Regio BR 245 Traxx DE Diesel loco with Dosto carriages in tow on a rapid RE3 service to Friedrichshafen. Radolfzell to Friedrichshafen is the only non-electrified section on the lines around the Bodensee, and this (gorgeous) tunnel in particular might be the sticking point to get the whole circuit electrified.
Nonnenhorn, Germany. DB Regio BR 425 on a RB93 local service between Lindau and Friedrichshafen about to leave Bavaria.
Bregenz Hafen, Austria. ÖBB Rh 4748 Desiro ML, likely on a S1 service to Lindau, about to pass the Nostalgiebad Mili.
Bregenz, Austria. Not a Bodensee train, but a chance at this station to hear the "do-re-mi" of an ÖBB Rh 1116 Taurus on start-up, pushing a Railjet service to Vienna, IIRC.
Rorschach, Switzerland. Appenzeller Bahnen BDeh 3/6 heads for Rorschach Hafen, the terminus of its S25 service. This one-of-a-kind unit runs on normal tracks and on the rack railway up to Heiden.
Ermatingen, Switzerland. SBB Thurbo RABe 526 GTW on a S1 local service from Feuerthalen to Wil, via Romanshorn.
Bodensee S-Bahn map. All the routes used on the trip, including Seelinie and Höribus buses, appear on this map. The network is across three countries and operations are split between DB Regio (Radolfzell-Lindau and the RE2 between Radolfzell and Konstanz), ÖBB (Lindau to St Margrethen) and SBB (St Margrethen-Konstanz-Stein am Rhein, plus the S6 between Radolfzell and Konstanz). Going around the large lake, the Obersee, requires seven different trains! But this can drop to five if you get a direct S7 service between Lindau and Romanshorn, which does exist, but operates most frequently on weekends (ad for the extended S7 on a Thurbo GTW below).
1, 2 or 3 countries in one train. With the S7 direct from Romanshorn to Lindau-Insel. No changes, under 60 minutes.
No train currently goes all the way around, but if I can have a brief moment of fiction, what would that look like? Well, all the tracks are standard gauge, electrified lines are on the same voltage, so there's just differences in signalling, which can be overcome as a EuroCity from Zürich to Munich uses the Bodensee route via Bregenz... and that pesky non-electrified zone between Radolfzell and Friedrichshafen. So a train capable of going around the lake would have to be a Diesel, a bi-mode or a battery-electric unit - on catalogue or already in the area, a German BR 563 Mireo Plus B or a Swiss-built FLIRT Akku would do the trick.