What a great question! As for how he knew which saint's day it was, does that come with his known source material? I'm having trouble deciphering text from annotation in this account of Holinshed, but that would seem to be a 'maybe'.

Which doesn't explain why he makes such a big deal of it ... I like the 'filial tribute' option, but with the caveat that we tend to regard as obscure things we don't know, and as obvious things that we do. If Will grew up observing the date of the professional patron - as a professional rather than a religious celebration - he may not have thought of it as an obscure reference.