Steve,
There are two types of pressure tank push buttons that I know of. I own one of each type of tank and have rebuilt them both. I’m guessing you have the older style tank.
The new button is provided for the newer tanks. You should have no problem rebuilding yours without it. Just stick to your aluminum shaft pump button.
I don’t remember exactly how mine went back together without having to put a hole in the diaphram, but my rebuild kit had the parts to allow me to do it so as to protect the integrity of the rubber.
