I infer from your response that, as far as you know, the answer to the question I asked is that there is not an explanation of Time::Piece::_wday in the module's documentation. In fact, none of the module's methods are explained in the documentation.

What is unclear?

The difference between Time::Piece::_wday and Time::Piece::day_of_week, for example.

Here's what Dave Rolsky wrote about Time::Piece in his landmark 2003 Perl.com article titled The Many Dates and Times of Perl:

Written and maintained by Matt Sergeant, this module is based on an interface designed by Larry Wall. It provides a convenient object API for datetimes, though the API is a bit confusing. For example, $time->mon returns the month number (1-12) while $time->month returns the abbreviated name of the month.

IMHO, because the API is confusing, the methods should properly be explicitly explained in the module's documentation—even those methods that, to an experienced computer programmer, seem plainly obvious from their names alone.