As pointed out by D.E. Knuth in `The TEXbook' this association
is done not before \output
routine time.
But the problem is not so hard to solve,
since in Th. Reid's version there is already a modified
\output
routine which decides if a certain figure will
fit on the current page.
As a by-product of this decision one easily gains
the information `odd' or `even' for the pagecount
of the current page.
So our problem reduces to the following simple decision:
\ifodd\count0 % \hbox to \hsize{\hss\copy\figbox}% \global\oddpagestrue \else% leftsetting \hbox to \hsize{\copy\figbox\hss}% \global\oddpagesfalse \fi% \ifodd\count0