I know the concept of a second team and also have one, Schalke 04, probably because it’s my dad’s team. I also have strong sympathies for St. Pauli, for the same reasons like yours, they probably have the most non-toxic fan culture in the (male) football world. Only for the rest of this season I’m rooting against them, because they are one of Gladbach’s main rivals in the battle against relegation.
ETA: and isn’t there a special club and fan friendship between Bayern and Pauli? It goes back to the time (late 90s?) when St. Pauli was in jeopardy of going broke, but Uli Hoeneß organized a friendly at their turf against Bayern for free whose revenues saved the club IIRC. This was one of the times that Hoeneß showed that he’s not always a total asshole and can be quite generous.