I don't understand the "would not think of wearing a Rolex" thing. I also worked for a fortune 500 company, well over 100 years old, and very conservative would be a massive understatement. The hierarchy when I first started in the 1980's made it feel like the office was stuck in the 1940's. The direction your desk faced, if you had a matt outside your office, if your office had carpet inside, if you had an office at all, right down to the colour of the phone you were given (brown or cream coloured) was determined by your "rank" in the company.
When we finally got rid of the suit and tie dress policy, one manager remarked "How will the workers respect the managers if we are not wearing a tie?" If you need a tie to get respect then you have bigger issues than a dress code, but this gives you an idea of the mind set there.
I wore whatever watch I wanted, and drove whatever car I wanted, and no one cared. I always had a nicer car and watch than anyone at my specific location, and probably nicer than the CEO had. Okay I can't say anything for sure about his car but have had lunch with him many times and he wore a cheap digital watch.
I don't know how "down to earth" a place can be if the watch you wear would upset your work colleagues.
😵💫