It looks like for some people residual inhibition can last from seconds to minutes, even hours. And this research paper hypothesizes that in some cases it may even be permanent.
A New Method for Assessing Masking and Residual Inhibition of Tinnitus
For me, at first it was just a few seconds but this morning I was experiencing a pretty massive spike where I couldn't even hear the TV over the tinnitus sound. I started messing with white noise, violet noise, pink noise, and a tone generator playing a single 10.7 kHz tone for a couple of minutes. After doing this my tinnitus sound initially disappeared, then after maybe 30 seconds came back at a low level and stayed that way for several hours. It then spiked again to how it was when I woke up. I just tried the same thing I did earlier and the eeeeeeeeeeeeeeeeeeeeeee is much lower now and has been for a few minutes.
I'm starting to wonder if maybe this could be a way to manage it while it's spiking. I have no problem playing a 10.7 kHz tone several times a day or even several times an hour if needed in order to reduce the shrieking noise for even a few minutes every once in a while.