I agree with all your points they are all valid and justified, additionally it could be his hope that she's going to accept him one day, the anticipation might have blinded his logical mind and must have made him simply go there without thinking much into the other details.
Giving him hope and everything is fine.
But this logic of he has to know the handwriting and touch of everyone is something which is beyond me.
Not everyone is blessed with that kind of memory and senses đ¤§
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