In short: You Can't.
The code for it is, in fact, not in the game. I use PKHeX to check if it was an item programmed into the game, and it was not. Screenshot:

There isn't any reason for it to be programmed into the game anyway, because Game Freak has no reason to program the V.S. seeker into a game which already has a method of rematching trainers.
Even if you took the data from the Gen 4 Sinnoh games for the V.S. seeker and manually programmed it into the base game, it probably wouldn't work, because the game is programmed to say "now isn't the time to use that" or whatever Oak says whenever there is an item the game doesn't know what to do with.
In summary, it has a 99% chance of not working even if you could hack it into HGSS.