Is there a thin silver metal ring around the glass lens? If so, look for a break in it, and use a fingernail or small non-scratchy flat-blade object to pull it inwards and then down, after which the glass lens will fall out allowing access to the bulb. If it's an MR16 bulb, the bulb and reflector will be part of the same unit, so pull on the reflector not the glass bulb.

Thanks. Do you know how long the light fixtures usually last? I'm assuming this one is 16 years old, thought it would be cost effective to replace now vs when water in our pool.

Once we got the light fixture down, I could see the manufacturer's name Lightcraft of California. I googled the name and found the patent application for the mechanism that attaches the globe to the stem. Now that I have that information, along with an exploded drawing of the internal mechanism, I'll be able to change the light bulbs in the future. As for the fixture itself, I found it for sale on several sites, including 1st dibs, where it had already been sold. Apparently, this 1960's fixture is very popular. Maybe because people like the look, but have not yet tried to change a burnt out bulb in ths fixture.

Been there...done that. I've moved a central light to two side lights (and oddly due to my wife's redecorating ideas back again). First word: if you have a splice, it needs to remain accessible. So if that box still has a live connection in it, you need to leave a cover plate (though you can paint or otherwise hide it with anything as long as you do not need to disturb the "finished surface" to get to it). The first thing to do is see if you can find where the wires run now. In my case I had the good fortune of having an accessible attic above and was able to pull the wire from the central box up and then fish it down to the closer of the two wall sconce locations. I then ran a wire from there to the other location. It wasn't necessary to cut any holes larger than the box size for the new sconces. Since the old box no longer had any wiring in it, I could cover it over with wall patch. If you're not so lucky, you'll probably need to be cutting into the wall to find and relocate the wiring. If we're talking drywall, this isn't a big thing. I've spent more time cutting and patching drywall over my life than I care to think about. You may wish or need to remove the mirror. Hopefully it's mounted reasonably rather than being glued to the wall (in the latter case you'll have a lot of drywall to replace :)).