If we're not talking about gas stations, it must be the other kind of station.
There were no stations with buildings. like the Radial Terminal, later the Bus Terminal, uptown in Hamilton.
The old Hamilton Northwestern Railway had 4 stops on the Beach. I understand that they were called stations, but I don't think that any of them even had platforms. The first one was where the railroad entered the Beach, the second was at Dynes Hotel, the third was at Elsinore, and the fourth was at the Ocean House, almost at the canal.
The railroad stopped providing local service, and local stops, shortly after the Radial Railway came to the Beach. It made several stops along the Beach, all of which were called Stations. When the Radial Line withdrew from the Beach and buses replaced their cars, the buses stopped at the same spots, and the Station numbers were kept.
I know that in the 40's there were Stations 4, 5, 6, 8, 9, 10, 12, 14, and 16. Some people might recall some that I don't, and I can't argue with them. I suspect that 1 and maybe 2 were before the cars reached the Beach. I don't know if there was ever a 3 on the Beach. Station 4 was at Huey Dalzell's store, 5 was at the little convenience store (but they weren't called that then) next to the Texaco Station a little south of the school, and 6 was just north of the school about where the new Shutters business stands now.
I never got on or off a bus further north of Station 6, so I don't know exactly where the others were, but when you asked somewhere where he lived he would say "near Station 8" or "at Station 12", and that was always close enough for me! I'm sure there are many people still on the beach who could give you exact information on the location of those north of 6.
I don't know if there were once Stations 7, 11, 13, 15, etc., and they were later dropped, or if they were never assigned, to leave room for future growth, the way Interchanges on our highways are numbered now, leaving room for more interchanges to be added later between the present ones.
I'm sorry I could be more helpful on this, and I look forward to hearing more details from those who do know!
Fred