I'm currently playing Pokémon Red on the 3DS virtual console and was excited to find that the old glitches were still in tact.
When I made use of the Long Range Trainer glitch on my original Red cartridge, I used Abra's teleport in Cerulean, but I never tried it anywhere else. I know there is another potential Mew using a north-facing Gambler on route 8, but when I tried this using teleport, when I return to the area, no other trainers will start a battle with me, and I have to reset.
The guide says to use fly, but also says teleport can be used to acquire Mew at the earliest point in the game, which I can verify. I don't know why it wouldn't be a valid way to initiate the glitch in any other area.