Not sure what you mean by gaps. If you take the entire wall out then you have a rectangular room

Are you redoing the entire bathroom? If yes, just look at photos that show the half wall.

Is this a stand alone vanity with a countertop? If not, what countertop are you using. One sink?

I think you have a gorgeous bathroom. Could you have carpenter retrofit the bottom part of the existing vanity with functional drawers and a center cabinet? It would be cheaper than tearing out the whole bath and losing that beautiful tile.

Thank you for your responses. I’m not able to find a way to edit my post so I’ll reply here. As much as we love our tiles bathroom, we have missing tiles from our kids hanging on the wainscoting. We will gut the entire bathroom and our contractor will plumb for 2 sinks. I’ve included dimensions of our 72 in Costco vanity. We have a 1952 rancher and the wall dimension on the right limits us to a vanity with 21 in depth. We will have 4 ft wainscoting of subway tiles.

We would like to keep the wall on the left and make it a 4ft pony wall for some separation/privacy for the toilet (see inspiration 3rd pic). Our issue is that the current space is 78.5 in. Our vanity is 72 in. Should we 1) enclose the vanity with 6 in x 4ft pony wall on left and same size drywall on the right 2) build pony wall on left and 6.5 in gap on right or .…. 3) remove the left wall completely and center the vanity with ~8in space on both sides? I hope I am not too confusing with the details of our dilemma. I appreciate any insight or alternative reccs. Thank you!

It would be ideal to build the wall so it exactly fits the vanity, but you're using a stand alone vanity in an area meant for a built-in vanity. Which means you'll have a 1 inch gap on each side of the vanity between the vanity and the wall due to the countertop overhang, and a back splash that doesn't continue onto the sides, where it is needed due to sink placement. If you are set on keeping this vanity, I'd remove the pony wall entirely so you have elbow room at the sinks, and can place it with a cleanable gap on the right. The toilet will still be partially blocked by the vanity.

I like the idea of removing the pony wall/separation. That will give your vanity the space it needs to look good and to clean around it.

I agree remove the wall if you can. Make sure it’s not load bearing!!
Enjoy!! Looks like a great space to work with.

How much space do you have from the wall to the outside wall? Or the space from edge the toilet to the wall? What I'm getting at, could the wall ne moved closer to the toilet?

Just a thought:

You might consider a pony wall that is vanity height. Place the vanity where it needs to be for the sink to be appropriately aligned. Then buy a countertop that is long enough to be "wall to wall" ... including overlapping the pony wall you create by cutting off the top part of the wall now left of your countertop.

Alternately, you might consider adding a frosted window from countertop height to ceiling so that you keep privacy but add light from the window.

The vanity is the pony wall. You need the width of the pony wall as breathing space so the vanity doesn’t look like you were trying for built in but mis measured. I’m another vote for keeping the existing tile and putting that money into a custom vanity that fits the space…

Makes me want to cry that your beautiful and unique tile bathroom is going to be destroyed. There are sites that sell vintage tile where you might be able to find replacement tiles for the missing pieces.
Just in case you change your mind, have a look here: https://retrorenovation.com/category/bathroom-categories/