Tell him to cap it the same way he'd cap the end of a piece of baseboard-- miter the end of the last piece of chair rail next to each side of the mirror, and cut a wedge shaped plug for the end, and then grout in the gap, just as was done at the end of the chair rail on the right in this picture:

Bill thank you so much for your insight on the thin set. I have opted to go with a row of subway tiles on top of the chair rail with a 3/4 round on top of the tile. This chair rail runs through the shower as well & I think it will be beautiful this way as well. The chair rail on one end of tub lines up with vanity marble top so aesthetically it should work out!?! Will post pics when tile is in.

I have stained trim in my entire house but not one piece of my crown is stained. That would stick out like a sore thumb in rooms with only 8' ceilings. Racing stripes is the term used in rooms that have all that horizontal stained wood. A picture would be helpful. Whatever you paint, make sure your crown and chair rail are the same color. Are your windows painted or stained? I would assume stained. If you keep the baseboards and door trim stained, then the windows are fine to stay stained. However, you may decide to paint the stained trim once you see the clean painted trim, and if you do, your windows would also need to be painted.

Walker Zanger 6th Avenue has a white gloss but not sure how white it is as I was focused on finding a blue. This is Walker Zanger's more "affordable", "quick ship" line from what I've been told and more affordable than most Pratt & Larson for example which I also looked at. (I'm using the WZ pale sky gloss in a 6" hex for a bathroom project that has yet to begin.) It has lovely mouldings and does have bullnose pieces. However, the mouldings are expensive, even in this more "affordable" line. Luckily I don't need any of the molding pieces. https://www.walkerzanger.com/collections/products.php?view=mat&mat=6th+Avenue&coll=6th+Avenue You could also consider Sonoma Tilemakers Stellar Quickship Collection which is also "affordable". In the Steller Quickship line, there is a "Blanco" gloss which is white (can't remember how white it is though) and there are lovely mouldings and bullnose to choose from. My mom used the 4x8 bossy gray from this line for her bathroom backsplash, including bullnose pieces. https://sonomatilemakers.com/stellar-quickship/ If you have more money to spend, Sonoma Tilemakers' regular Stellar line (not the quickship) has "Pure white" in addition to "Blanco" and even more liners and mouldings to choose from. https://sonomatilemakers.com/stellar/ To give you an idea of pricing, for me, the WZ 5th avenue 6" hex is approx $24/sq ft (w/o contractor discount) or $19.50/sq ft w/discount. The WZ 3x6 bullnose is approx $9.50 per piece (w/o discount) and base moulding is approx $21 per 4x8.5" piece (w/o discount). Sonoma Stellar Quickship (for the bossy gray color at least) was approx $18/sq ft for the 4x8's (w/o contractor discount or $14.50 w/discount) and $25.50/sq ft for a non-quickship glaze (w/o contractor discount).