But I noticed a side-effect: if I then turn off the tone generator, my tinnitus would disappear! Unfortunately that effect only lasts for a minute or less, so it is not really practical to get relief this way.
Note that I would be careful about using pure tones for too long. Pure tones end up focusing the energy in your cochlea towards a small area of hair cells. Since these cells don't regenerate, it may be wise to avoid overstressing them.
My tinnitus is fortunately not super loud; it's only noticeable when it's relatively quiet, or I'm blocking sounds (with ear plugs, or noise cancelling headphones without input, etc.). So it's not like I habitually blast my ears with loud sine waves out of desperation. But I can imagine it may be different for other readers, so that's a good caveat.