LanX:

In the page you linked, it looks like lines 1612 and 1613 (inside subroutine maybe_my) fetch the information from the PAD if it's a typed PAD:

1607: if ($op->private & OPpLVAL_INTRO and not $self->{'avoid_local'}{
+$$op}) {
1608:        # Check $padname->FLAGS for statehood, rather than $op->p
+rivate,
1609:        # because enteriter ops do not carry the flag.
1610:        my $my =
1611:            $self->keyword($padname->FLAGS & SVpad_STATE ? "state
+" : "my");
1612:        if ($padname->FLAGS & SVpad_TYPED) {
1613:            $my .= ' ' . $padname->SvSTASH->NAME;
1614:        }
[download]

I didn't dig any further into it because it looks like the right thing. Hopefully that'll get you on the trail to the info you're looking for.

Note: I got lucky when looking for it, as I first did a ^F in the browser looking for my, but it indicated over 1000 results. However, it also added highlights, drawing my attention to the first item: OPpTARGET_MY. Changing the search to _my gave a mere 6 locations, and the third one shows where the type name gets added to the "my TYPE VAR" output for Deparse. Had it not done so, it may have taken a while to dig it up.

...roboticus

When your only tool is a hammer, all problems look like your thumb.