Given that Jeph has called this "Elliott is Cute Week" on his Twitter feed, I feel confident in predicting that we are going to be sticking with this arc at least until Friday. However, what will happen?
I'm expecting that Renee will tell Brun that she can't act on Elliott herself because he's attracted to Brun. I suspect that this will come as news to Brun. That said, I may be doing her a disservice and she might be fully aware of Elliott's reasons for wanting to pat her head. The big question will be whether she reciprocates.
Either way, I've got a feeling that the latter half of this week will be Renee and/or Brun making Elliott very nervous by tentatively trying to work out if he is really interested in them and maybe even flirting with him in a tentative and somewhat amateurish manner (or at least behaving in a manner that you could interpret that way). Naturally, Elliott will get locked into an indecision loop about whether he is reading too much into their behaviour.
If Jeph feels like it, he can probably sustain such a holding pattern for months. However, if it's Brun who is doing the flirting, it is much more likely that she'll lose patience in the whole thing and just directly tell Elliott what she wants and what she believes he wants, leading to the proof that Ellliott can do a full-body blush.