The rod is typically held into the center of the piston by a small crimp or "stake" mark on the top edge of the piston hole.
The Heat Method: Sometimes, old fuel varnish is the only thing acting like glue. Soaking the assembly in a strong carburetor cleaner or applying very gentle heat to the brass piston (not the steel rod) can help break the bond.
The Press/Punch Method: Use a very small drift punch that is slightly smaller than the diameter of the rod. Support the piston on a block with a hole in it (a nut works well for this). You gently tap the rod through the piston from the top.
The "Drill" Method: If the stake is heavy, some technicians use a drill bit slightly larger than the rod diameter to very lightly "kiss" the top of the piston. This removes the crimped brass lip, allowing the rod to slide out.
Once you have your original rod cleaned up, you’ll slide it into the new piston. Since the new piston won't have that factory "stake," you have a couple of options:
Re-Staking: Use a small center punch to lightly tap the edge of the brass hole on the top of the piston to "pinch" the rod back into place.
Adhesive: A tiny drop of high-temperature, fuel-resistant thread locker (like Red Loctite) can work, provided the surfaces are surgically clean of all oil and fuel residue.
Check the Spring: While you have it apart, ensure the power piston spring isn't compressed or distorted. It needs to have enough tension to push that piston up when vacuum drops.
Vacuum Bore: Before installing the new piston, make sure the bore in the carburetor casting is perfectly smooth. If the old piston was sticking, there might be a burr or "glaze" in the bore that needs to be cleaned with a bit of Scotch-Brite.