You can immediately book a new one through the normal process (you'll pick a specific attraction and get the next available arrival window), plus you get a wildcard reservation that you can use for a different attraction (or the same attraction once it gets back up and running) without needing to schedule anything.
The wildcard reservation can't necessarily be used for ANY ride you want, depending on the park. Like... if Imagination breaks down, you're not going to be able to redeem the wildcard at Ratatouille. They're tiered based on what's the most in-demand attractions, similar to the old FastPass+ groups. At Magic Kingdom however, all of the Genie+ attractions are in the same bucket.
The wildcard reservations are not subject to the one-per-day limit. So if you use a Lightning Lane at Big Thunder, and then Buzz breaks down, you can use the wildcard reservation to ride Big Thunder again.
I always thought this was the case, but that was not what happened over Easter. We got the wildcard, but not the ability to immediately book another attraction. (I tried!)
What did happen though, was something else a bit quirky. We had Space Mtn, it went down, got the wildcard. I attempted to book next pass, but no go until our previously anticipated time. Space Mtn came back up. At our next booking window, 3:10pm, I booked a 10pm Space Mtn. At 4pm, we attempted to use our anytime pass to ride Space Mtn.
The Space Mtn G+ queue was FULL all the way out to the exit of Space Mtn. I felt REALLY bad for folks in the standby queue. We did 1st scan at 4:07pm, and 2nd scan at 4:27pm, exited ride at 4:40pm.
When we got off Space Mtn, I discovered we were THEN able to book our next G+, but it was still a few minutes before our 2-hour window. (I set an alarm). A little while later, I realized we no longer had the 10pm Space Mtn pass, but we still had our anytime pass.
Alas though, we wound up getting some decent G+, so we didn't end up using the wildcard pass until 10pm, at which time the park was empty and the rides were walk-on. HM was posted at 45, but it was walk-on. Earlier in the day, waits were VERY HIGH, but at 10pm, the park was empty.
I have booked plenty of re-bound passes in the past.
