Welcome to BOL, MHansen!
Don't make the mistake of labeling this matter an "ESIGN issue" and manage it like a legal/regulatory requirement. The FDIC Bulletin Randy cites is safety & soundness guidance, not compliance guidance.
ESIGN sets a standard for the delivery of e-documents, but not for digital signatures. The ESIGN Act declares that e-signatures are legal and binding, BUT contains no definitions or rules for using e-signatures. You have to supply your own definitions and rules, and that's where FDIC's guidance begins.
You step into a new type of business risk if you allow digital signatures instead of wet signatures. While there are a few state and federal laws/regulations that require you to obtain the customer's signature, the main reason you get a signature is to prove (in court) that your customer is contractually liable for performance of the terms of the contract. Lenders are painfully familiar with the losses that can result from missing or forged wet signatures on loan documents. Mitigation techniques are also well understood. Even in the extreme cases of illiterate borrowers who sign their name with an "X", there's an established way to do business safely.
In the digital world, the loss mitigation challenge continues to be -- "prove it!" You will need airtight evidence that this borrower's digital "X" on these loan documents is, indeed, his/her "X." You will need this same evidence for as long as need to be able to sue the borrower for breach of contract. Like children, your self-developed standards for proving e-signature validity remain relevant for the lifetime of the loan.
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...gone fishing.