Not seen one like this, so how does one replace the battery in it? The cap with logo does not appear to turn off, pop off and I'm not about to experiment. Anyone had experience with this type?

Side view....

OK, don't bother calling Cartier.... they were not any help. Suggested I send the clock to them.

So, upon further examination, the gold cap has to be pressed down with a good deal of force and then turned clock-wise about 20 degrees. Then the entire cap comes off and below sits the battery... an LR50. It's about as tall (or taller) than it is wide!

Persistence paid off!

That's about as much technical expertise as you can hope for with today's timepiece salespersons you are likely to encounter in a jewelry store . . . that they will know how to change the battery. However, you don't always get to that level, as your experience shows.