Hmmm. But if it is part of the same structure that is containing all the radiation in the first place, then discovery of one of the "radioactive tendrils" that gradually increases in intensity the deeper you go should be enough. Like at the surface you should feel ill, and there is a plate. Maybe on the plate, it has a symbol indicating intensity, like a wifi intensity indicator.
If you go deeper you get sicker, and you find there is an intensity indicator with the next level filled in.
Like if the structure itself will be there in 10,000 years, then making part of that structure protrude to the surface with some sort of intensity indicator that changes along its depth, as graduated exposure to radiation increases, should be pretty clear.
People undergo radiation therapy as a cancer treatment and they feel nausea but it's not a lethal dose. ChatGPT seems to think that:
Recovery from Mild Symptoms
At a dose of 0.5–1 Sv, symptoms such as nausea, fatigue, and possibly mild skin reddening may appear within a few hours to a day after exposure.
Recovery is likely within days to weeks as long as there is no further radiation exposure and the total dose does not exceed the body's capacity to repair cellular damage.
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But then it's just a machine so obviously one should consult a nuclear physicist before actually implementing this in a multi-millenia nuclear waste containment site
When it comes to old nuclear material, it's more the danger of getting radiactive particles on and in you than it's about pure radiation. You can walk away from a machine but you can't walk away from that fine powder you just inhaled.
For a real life example: https://en.m.wikipedia.org/wiki/Goi%C3%A2nia_accident It was finally clocked as harmful 15 days after they got a hold of it, plenty of time for lots of people to get a lethal dose. And these people probably had at least some pop culture knowledge of nuclear radiation, compared to a distant primitive civilization who would have nothing.
If you go deeper you get sicker, and you find there is an intensity indicator with the next level filled in.
Like if the structure itself will be there in 10,000 years, then making part of that structure protrude to the surface with some sort of intensity indicator that changes along its depth, as graduated exposure to radiation increases, should be pretty clear.