Quoting the esteemed tax practitioner, Elmer Fudd, willfulness is a “wascally” little word.

What burden of proof will the IRS apply in deciding whether a taxpayer has truthfully certified non-willful conduct: Preponderance of the evidence, or, clear and convincing proof ? That remains to be seen.  The non-willful certification process appears to place the burden of proving non-willfulness on the taxpayer. However, one should not forget that the IRS bears the burden of proving willfulness in an FBAR civil penalty suit.
Without further guidance we might just have to settle for the good old phrase......... " I know it when I see it ".
Notably absent is any discussion on the role of willful blindness (or similar formulations, such as deliberate ignorance) and whether it even applies within this new framework. The theory of willful blindness permits the trier of fact to infer willfulness. Instead of proving that the defendant intentionally violated a known legal duty, the government need only show that “the defendant consciously avoided any opportunity to learn what the tax consequences were.” United States v. Bussey, 942 F.2d 1241, 1428 (8th Cir. 1992).
In other words, it is a “watered-down” substitute for the burden of proof on what is otherwise the most serious element of a criminal offense – the mens rea element. Because willful blindness is much easier for the government to prove than willfulness, most courts restrict its use.
Presumably, the definition of non-willfulness, as quoted, excludes willful blindness. Why? Because willful blindness is inconsistent with the IRS’s definition of non-willful conduct. For example, a taxpayer who consciously avoids learning about his obligation to report foreign financial assets is not one who fails to disclose such assets due to a mistake or a good faith misunderstanding of the tax law. Indeed, the former has a sinister motive while the latter is innocent. Stated otherwise, if willful blindness had been contemplated, the IRS would not have defined non-willful as narrowly as conduct that was due to “negligence, inadvertence, mistake, or a good faith misunderstanding of the tax law.”
One way to view the path between willfulness and non-willfulness is on a continuum. The facts of some cases will present themselves on either end of the continuum. In those cases, recognizing whether the conduct is willful or non-willful will be as easy as finding a free drink in Las Vegas.