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They'll either introduce a completely new character to do this, or they'll have the rival bombard you with longwinded and overly roundabout text dumps that amount to the developers just gong "Hey player, expect a sequel soon."
For example:
>"Hey, anon. Do you know what deja vu means?"
>YES
>"It's that feeling you get when you think you've done something, seen something, or been someplace before, right? Well, this whole adventure seems rather familiar to me. Heh, maybe I was a Pokemon Trainer in a past life as well! What do you think, anon? Anyway, Professor Oak told me that there is an old legend of a mysterious Pokemon with the power to travel through time. But it lives in the Johto region. Maybe we'll go there someday too, huh? Time will only tell, right anon? Welp. Seeya!"