I may have done a double-take when I got this invitation. Third Rail Projects, the immersive theater company behind shows previously staged at a Bushwick warehouse and a Williamsburg church, was announcing its newest piece, “Ghost Light” … soon to be presented “at Lincoln Center’s Claire Tow Theater.”

Third Rail and Lincoln Center? It’s an alliance that sounds unholy at first blush, but ultimately proves felicitous.

In show biz parlance, a “ghost light” is an electric bulb left illuminated on stage in an otherwise empty theater. The notion has some eerie associations, and that’s the idea Third Rail is toying with here: Theaters are filled with ghosts, of one sort or another.

The Third Rail formula is familiar, especially if you’ve been to immersive exploratory events such as “Sleep No More.” A group of patrons enters a space (in this case, we began as an assembly of about 100) and is fast whittled into smaller units. Each group follows a different track, guided by different actors.

All theatergoers get roughly the same experience, but not in the same order. With “Ghost Light,” most of the show takes place backstage in the actual dressing rooms, prop storage areas and stairwells otherwise used by real cast and crew working at the Claire Tow.

A pale young man was the sole actor in the closet-sized space where the show began for me and a half-dozen others. He set the mood with a story about an apparition said to cross the stage each night at roughly the same time at theaters in London and New York. “Lately,” he said in conclusion, the same fella has been seen in Lincoln Center.

Got your goosebumps? So, it’s this that establishes a key point: Everyone we’re about to encounter is probably dead, including the guy telling us this tale. But that doesn’t mean they’re not friendly. In one room, the theater janitor treated me as a new hire, cautioning me to punch my time card if I wanted to get paid.

Some of the segments evolve into indulgent performance art pieces that unnecessarily bog down “Ghost Light.” You can end up spending too long watching actors in a preening, overly theatrical ballet-ish sequence. This also has been an element of Third Rail’s previous shows, “Then She Fell” (2013) and “The Grand Paradise” (2016).

On the other hand, Third Rail is more liberal here letting audience members “get our hands dirty,” something I wasn’t anticipating backstage in the rareified, highly managed air of Lincoln Center.

Are there insurance implications to having me operate heavy props by rope and pulley? Do I get my Equity card for speaking Latin—um, maybe it was Pig Latin—in the Shakespearean side show during which I was somehow “cast” as a Friar and sent wandering around with a 4-foot-long scepter?

As with Third Rail’s other productions, there are a few “sections” that not every group will experience. You end up discovering this in conversation with your mates after the show: “You were in a room with whom doing what? And she was playing piano?”

Third Rail fiddles with ideas that are inherently interesting: “Then She Fell,” still running, had us roaming a Lewis Carroll-inspired psychiatric ward; “Paradise” took us to an eroticized Fantasy Island. So tell me, what theatergoer wouldn’t be enticed by a backstage pass to this opulent venue, seasoned with just a touch of the supernatural?

“Ghost Light,” on sale through Aug. 6 at Lincoln Center’s Claire Tow Theater, 150 W. 65th St. Tickets: $30-$50. Call 212-239-6200.

Follow Robert Kahn on Twitter@RobertKahn