The ESIGN consent mechanism is unlike any other set of rules. ESIGN has no "life of its own". Instead, it comes into play when some other regulation requires the delivery of "written" documents, disclosures, notices, etc. If a rule (Reg. E, for example) requires "written" disclosures but you want to substitute electrons in place of paper, then you pull out ESIGN and follow its procedure for obtaining the customer's consent for the substitution.
If your bill pay and ACH services trigger Reg. E or other state or federal disclosure requirements and these disclosures must be provided "in writing", then you will need the customer's consent--via ESIGN.
Many banks set up their ESIGN consent process to cover a wide range of documents and disclosures (so they wouldn't have to keep doing it again and again as new e-delivery opportunities arise.) Review your ESIGN process & see what you & your customers have already agreed. Maybe the existing consent is broad enough to cover what you need.
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...gone fishing.