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It's hard to say what that mouthpiece is from the picture. Even under magnification it just looks like a round gray blur.

I believe I may have found one…(??)
Maybe, there’s not enough tea in them to avoid getting lost in the music…??

I have the twin to that one, an Olds Ambassador alto horn/altonium in F; the serial no. dates it to 1956. A small shank trombone mouthpiece will "sorta" fit it, but I found an alto horn mouthpiece for it. We've even used it at TubaChristmas so a French horn player could participate. We had an over-enthusiastic band booster president who was forever "winning" horns on eBay, having them overhauled, and then donating them to the band program. One day she proudly presented us with a "little baritone". It was pretty awkward telling her that we couldn't use it and why. I forgot all about it until later that year when I retired. At my very last spring concert as a band director, she stepped up and placed it in my arms (it was on top of a very fancy-decorated grapevine wreath) and said it was my retirement present. I started laughing and couldn't stop and conducted the last concert selection of my teaching career giggling the whole time. My wife later made me throw away the wreath. The horn makes a nice conversation piece in my office, though.

It is funny (and remarkable) how the alto horns tolerate different mouthpieces. The traditional way is with a cornet-style mp, preferred by trumpet players doubling. But there are french horn style mps with the bigger shank for the french horn players and, if the receiver is wide enough, you can use a trombone/baritone mp like I do on my two altos. But in most cases you can't hear which type is used and you can mix different players without problems.