Like everything else, most of this will depend on the fictional situation. Because of that, I will usually ask the players to explain just how it is they are helping or interfering. In some cases it's obvious - in your case of two PCs simultaneously trying to read each other, it's generally pretty clear that we're talking about peoples' poker faces and convincing lies and deft evasiveness. There are exceptions, and these are where I'll want the PC to step in and explain their actions, as that will inform the consequences of success or failure, either of the interference or of the reading itself. But asking someone to say how they're helping or interfering is totally fair game, and if they can't tell you, don't have them make the roll - to do it, you have to do it.
FWIW, flipping someone's move is a pretty natural consequence of a badly-miffed roll to aid or interfere. So if you're trying to help and fail, your "help" comes out as interference and the target takes -1 or -2 forward instead. Similarly, if you're trying to interfere and fail, you inadvertently create an opening or give something away and the target takes +1 or +2 forward against you on their roll.
Example: Deke (the Battlebabe) and Major (the Hardholder) are undergoing tense negotiations about the parameters of the bounty hunt that Major wants Deke to undertake. Both suspect that the other is holding something back, and both want to read the other. But these two characters know each other, they have a long history of not quite seeing eye-to-eye. Both players decide to interfere with the other, and thus both roll+Hx. Deke is Hx+2 to Major, and Major (who holds things closer to the vest) is Hx+1 on Deke's sheet. Major gets an 8, Deke misses with a 5. So Major is taking +1forward from his partial, and the MC says that Deke's miss will be represented by her having a shitty poker face - he flips her move and gives Major a further +1forward.
Alternately, the MC could have decided that Deke's failure meant that she was interfering with herself, i.e. that she was overthinking the conversation, reading too much into what Major was saying, getting analysis-paralysis, and that she would be taking -1 or -2forward on the next roll. This too would be a flipped move, and I think either way is fine. Much will depend on if it is understood that Deke is also about to make another roll.
Now for the read a person roll itself. Major is Sharp+1 and is taking +2forward, and easily nets a 10. Deke rolls (she's also Sharp+1, but has no modifiers) and with a 4 misses this one as well. Not Deke's day. In the ensuing conversation, Major gets to ask three questions that Deke's player has to answer honestly. And if this snowballs into another move(say into a manipulate roll), Major will take +1forward against Deke if he acts on this information. Deke gets to ask 1 question (which Major's player has to answer honestly) which may also give her +1forward, but now she must prepare for the worst. Given that Deke's roll was a miss, the MC is typically encouraged to make a move here to reflect the situation. Since at this point it's just a conversation between the two, my gut instinct as MC is to keep the consequences tightly tied to the interaction - it is clear that Deke has a pretty poor read on Major, and maybe that makes her rethink her entire understanding of him as a person; I'm going to take away her stuff and drop her Hx with Major by two points (so now she erases the current value and writes Hx -1 next to his name).
Thus, all of the misses have consequences that fit the fiction. The MC interjected his own moves into the mix, but they were direct and largely mechanical in nature because this was about the PCs interacting with each other rather than the environment; heavy narration wasn't warranted, and indeed might have been a distraction from the players mutual spotlight.
Does this make sense?