Actually I did work overnights on a station that did zero syndication. It was a 6 hour shift and 2 hours of production. I got calls and got to know many of the listeners (mostly shift workers and college students). No, it wasn't a huge audience but I noted caller's favorite song, where they worked and if I found out, their birthday. I said hello to places that regularly listened, dropped names on favorite songs from time to time and tried to create a feel that we were all this big family. I did not stay in that shift a very long time mainly because my PD did the morning show. So I got added attention and 'aircheck sessions' the other shifts didn't get. My problem wasn't staying awake during the shift, it was getting enough sleep because my PD would hold a meeting at 10 or want me to join a live 2 or 3 hour remote at 3 or 4pm. And back to work with production at 10. It was always something once or twice a day.
The truth was I was lured to the station for the 7 to Midnight shift but was told on I got there I had to start on the Midnight to 6 shift until I got good enough for a better shift.
I worked overnights for many years, and my experience was NOTHING like that. I can only guess that you did this in the '70s or '80s, when the audience was actually still there. When I worked overnights at WCMT, they carried Larry King Live, on both AM and FM. I'm guessing that they did this because the AM was pumping out a whopping 54 watts at night. But I seriously doubt that very many listeners heard it, because AM listeners (mostly my parents' age at the time) had gone to bed, while FM listeners just flipped the dial in search of music. After I left WCMT, Larry King moved his show to late afternoons. They got complaints about that from AM listeners, from what I understood at the time, but he was off of FM once he moved to late afternoons.
My next station, the old WDXN, was even worse. I did weekend overnights there for a few months, and I am positive that we had ZERO listeners during that time frame. As I said earlier, I asked for syndicated programming during that time slot, but they wouldn't hear of it. I should point out that, at that time, they had only recently started broadcasting 24 hours. They later added an FM sister station to simulcast with it, but its tower was in a very rural area, so probably did very little to increase listenership, especially during weekend overnights. But again, the problem solved itself after I left. The GM was hit with a sexual harassment charge, and was soon shown the door. After that, the station underwent a much-needed management and format change. (I know that this GM wanted me out, but even if I had somehow been able to stay, I wouldn't have been able to weather the changes that took place after I left, anyway.)
The solution for me was to program shortwave at night. It was worldwide, so we actually had listeners. I still had the local AM to program, but I got them to streamline the programming there as much as possible, so that I had little more to do than just babysit the programming, and drop the legal ID every hour. And I did all that for 10 years.