> "Any chance I can get an ETA on having that fixed?” This is the most annoying question in the world. I usually want to respond "probably sometime before the heat death of the Universe, but honestly that could slip". Until I write the fix I have no idea that the direction I'm taking will actually work. Very often I discover some $SADNESS while trying to actually do the fix. Some test may blow up in some way I never…
But this is exactly the information that other people need to plan around to get on with their own work. You need to see things from their perspective. The inner workings of your processes and the long-winded explanation, from their side, is "the most annoying" response in the world.
It's a simple question. The ETA is the only information that is actionable for them. If the answer is "anywhere from a couple days to a month", then flat out say that. If you think that sounds wishy-washy and absurd and that it must then require a long-winded explanation to soften, chances are that it does sound absurd and the long-winded explanation will not soften it, but instead the person may start to think that you are unorganized and clueless. They might start to cringe at the thought of their next interaction with you. Just give them a straight answer.
FWIW, I don't know anything about your system, but it sounds like you need to invest in making triage in your system more efficient.