Instrument markings back then were painted with luminescent paint containing radium, so they would glow in the dark continuously without having to be energized by a light source.
You can buy luminous watches today with the same feature that use tiny vials containing tritium gas for each marking (much less radioactive than radium and produces negligible amounts of radioactivity, so the watch can't hurt you). These also glow 24/7, but tritium has a shorter half-life and they lose about half their brightness every 7 years or so.
The radium paint was mostly a danger to the women who painted the instrument faces, who would lick the brush tips to get a fine point and could potentially ingest enough radium to develop radiation poisoning.
The radioactivity warning signs may be perhaps a little bit of overkill since the actual radioactivity emissions aren't that high and most of the risk is from ingesting radium directly; it's advised to avoid opening an instrument and poking around without appropriate precautions (If people knew the amount of radiation they're exposed to just being out in the natural environment, they'd probably want to move into a lead house. I recall a story about a 3 Mile Island Nuclear employee who was setting off the radiation detectors at work while coming IN to work, not while leaving. From some kind of radiation exposure while off work.) .