The valve gear for John English steam locomotives was made by Central Valley, and was an add-on kit.
The connection between the main rod and the crosshead is a hollow rivet, and the hole should be 1/16" (.625" - roughly halfway between a clearance hole for a 00-90 screw - .0520" and that for a 0-80 screw, which is .0670").
John English dates back to the mid-'50s or earlier, and is long gone. I doubt, too, that Central valley would have any rivets left from so long ago, but you may be able to get some suitable rivets from Bowser.
You could also make a hollow rivet using 1/16" brass tubing. Drill out the centre at one end of a length of tubing, using successively larger bits in a pin vise, until you’re left with a piece of thin-walled tubing.
Punch a slightly larger than 1/16" diameter circle from some fairly thin (.005") brass sheet, then solder that to one end of the tube.
Place the capped piece of tubing on a hard surface, with the capped end hanging over the edge to avoid deforming it.
Using a utility knife or your X-Acto, place the blade on the tubing at a point which will cut a piece of the capped end from the tubing, yielding a rivet as long, or slightly longer, than needed for the repair.
Now, carefully use the blade of the knife to roll the tubing back and forth, scoring its circumference while preventing the blade from wandering. Continue this operation until the rivet is cut free - it doesn’t take long.
If necessary, clean-up the cut end of the rivet with a file and, if needed, file the rivet to a suitable length - it needs to be long enough to protrude through the parts being joined, with some extra length to be deformed by placing pliers over the assembly, one jaw on the soldered-on head, the other on the open end of the tube. A gentle squeeze or two should deform the open end enough that it can’t back-out of the con