Often stage management positions are not posted at all, but found by sheer luck.
Because so much of the opera business is based on freelancing, it's important to be proactive and fill your own calendar. That's why I find Opera America to be very useful to find performance dates, staff listings, and websites. I can find shows when I'm available, companies I want to work for, and who to address my resume to. I can write a very specific cover letter about the show and why I want to work on it.
And if I don't hear back, that's OK, because at least I put it out there and tried. And it's one more production manager who has seen my name and my resume. But if I do hear back, it's another company I've made a connection with and may be higher on the list next time. And I might have gotten my resume in the week before they thought about needing to post for that position, or right when someone backed out.
Production Managers for opera are ALWAYS looking, even if the current season is staffed. The shorter seasons are hard to keep staffed, and could be needing someone. The festival seasons involve so many people, often someone backs out a month or two before.
So I don't wait for a job posting to apply for a position. If they're doing a show, they need a SM. The worst that happens is they throw it away, or maybe keep it on file. Or, if it all works out, they hire me before it ever hit the boards that they were looking.