On the subject of radioactive luminous timepieces, I noticed an interesting video where somebody looked at Geiger counter readings for an alarm clock with a luminous dial bought in the USA in the 1960s:
In the video the background CPM (counts per minute) starts off at 36 and jumps up to as high a reading as 6785 when the alarm clock is put next to the counter, nearly 200 times the background count. I don't know if this represents a typical alarm clock from the days when radium material was included as part of the luminous paint. The practice of using radium paint was more or less discontinued by about 1970 in Western countries due to health and safety regulations for manufacturing of the timepieces becoming stricter, which made the use of radium paint uneconomic. After 1970 the luminous paint consists entirely of a phosphorescent material like zinc sulphide, which is less effective and requires 'charging up' in daylight. Watches which use radium paint would have only a small fraction of that applied to an alarm clock.
I don't recall ever seeing the Greenies ever run a campaign against radium paint, even back in the 1970s. The Greenie version of radiophobia is specifically targeted at predominantly one industry, the nuclear industry, though they also run a less well-known campaign against the use of radioactive material in the space industry (some space probes and the recent roving vehicle landed on Mars use atomic batteries). Other industries that use, or have historically used, radioactive material in some way seem to get no hassle from the Greenies.
Most clocks and watches that have a luminous dial which includes radium paint will have been thrown away by now, and will be sitting in landfill sites. The only watches that might have some radium paint in them that are still in circulation are likely to be expensive watches (brands like Rolex) manufactured before 1970 that tend not to get thrown away.