Timing a 12(c) motion is a bit tricky.
By definition, you raise it after your would normally file a motion to dismiss, as the pleadings are closed. You can file one as late as you want, as long as it's "early enough not to delay trial." Honestly, I'd never seen a motion denied for being too late—until now!
The defendant in Ecolab Inc. et al v. DuBois Chemicals, Inc., C.A. No. 21-567-RGA (D. Del. Oct. 25, 2023) filed a motion for judgment on the pleadings at the same time as its SJ and Daubert motions, which was about 5 months before trial. Neither party devoted more than a few of their 40 allotted pages to the 12(c) motion—focusing instead on the SJ and Daubert issues.
(Note—the parties managed to fit the 12(c) motion briefing into their overall page limits for "dispositive motions" in the scheduling order. I think that's probably correct, but I've never seen an opinion actually addressing whether a later-filed 12(c) motion must adhere to those limits. It certainly looks like gamesmanship to give yourself an extra 20 page brief at summary judgment time, but what about a 12(c) motion filed 6 months earlier? Would those pages need to be deducted from a later SJ motion page count? I encourage someone braver than me to give it a try and see how it goes.)
Ahem...
Judge Andrews was having none of it and ...