A friend of mine inherited about 1,000 vintage clocks.

He set up shelves all around his bedroom and put them in the shelves and put his bed in the middle.

5 years down the track I made a joke about radioactivity from the glow paint. We realized it wasn’t a joke.

He got a radon gas monitor and it did register high.

He seems fine but doesn’t sleep in that room any more.

It depends on what sort of tinkering. The highest risk is if you open the case, which is likely to release some radioactive dust.

This. Sitting several feet away with the radium behind glass, you're down near background [1], but any contact with the dust is a risk. If you must to open the case, I would suggest doing it outside with mask, gloves, and eye pro: blow the case out with some compressed air to dispel any lose dust. Don't grind or disturb the markings otherwise. You can also replace the hands with non-luminous ones.

Also consider leaning in! Radioactive antiques and minerals is a whole fun hobby by itself; start with a cheap Geiger counter and move up to a scintillator for more fun. There are many artifacts like uranium glass, ceramic glazes, and watches to look for in antique shops.

https://www.kensclockclinic.com/vintage-clocks-and-radium-ri...

Agree. Radium is also an issue with vintage watches. A few years ago there was a paper discussing the the dangers of radon gas emitted from vintage watch dials. The tldr is keep them in a ventilated space. https://www.northampton.ac.uk/news/wwii-military-watches-pot...