Welcome to ESIGN! Any required federal disclosure that must be provided "in writing" must reach the consumer in a timely manner in one of two forms:
1. paper, or
2. ESIGN-enabled electronic documents
Since the whole idea of online account opening is to avoid paper (and the delay caused when the paper must be mailed), then (if not already accomplished) you will need to insert the ESIGN "informed demonstrable consent" process into the stream of clicks leading to a newly opened account.
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...gone fishing.