Assume a low-tech scenario, no Electricity, more or less iron age tech-levels.
Some people in this world carry devices the size of a modern compass. Within is a very thin (like hair, but of lighter color) wire, which is normally straight but bends in the presence of certain dangers (more or less radioactivity).
NOTE: Somehow you can see the wire and its state day and night with the naked eye, so that's not the problem. The function is also not impaired by the devices rotation etc.
That's all fine and dandy, but how would they notice without paying close attention 24/7? I do not know a way of translating this very small movement to something which would alert a human, much less so when sleeping.
Are they doomed? Do they have to stare at the device (at least one of the group) all the time, or is there a low-tech-way to "amplify" the warning?