2 handshake glitch doesn't exist.
I think people were just referring to it as a glitch within the glitch as an easy way of phrasing it. It was after one of the small updates (Halloween day I believe) that mine went from the handshakes piling up as people visited to needing to synch between each tap to receive the extra tile. If I did between each tap, the handshakes continued to pile up. But there really wasn't a point to leaving them there if I was in my town so I cleared the extra when I saw it.
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I just tested it out and now I have three handshakes. Thanks for pointing this out! I just crossed the threshold past the 150 mark, and so I will not be able to restart a tile if I accidentally tap the last one. Now I know I can leave two. I just need to check in often enough that not too many neighbors come visit in the same interim.
So, just logging in and out of your town resets it so that you can stack up multiple handshakes...or so it appears.
Thank you and TonyMinetana and speleo106 for pointing this out!