This is more of an FYI for others looking for this info.
Finally got somewhere. Following Walt’s advice above, I had to remove the carb to see anything at all, and once I got the grime off I could see that it was a Tryton.
Typing this name into Google eventually got me to TSracing and their parts catalog, where I learned that there are two different versions of this engine. A 125cc and a 118cc. The first one has a TX designation and the smaller one is called a VX. They have different gaskets for the reed-valve to block and the reed-valve to carb connections.
Here is how to tell what you got:
Look on the front of the engine, lower side near where the engine mount is, and you should find a number. If that number is above 1000 it’s a TX125. If the number is below 1000 it’s a VX118.
You can also look at the top of the crank case near the reed valve opening there may be a letter “T” stamped in the case. This means you got a TX125.
I found the T and it looks like this:
(Well, it would look like this if I could get the picture posted. But I can’t, so you’ll just have to imagine.)