Gene, Am in same boat as you. The only thing I could find that seems to fit the bill is through full tilt karting at the englishtown raceway. I am headed there Saturday to speak to them and go round in circles on their tag kart. They seem to run more than just arrive and drive services. I will ask about racing leagues etc. for us older farts (I am 47) and will let you know what they have to say.
Go there Saturday and rent a TAG kart from Full Tilt and run it to get an idea of karting. Talk with Full Tilt, they are a Tony Kart dealer. As for your age, I’m 52 and racing the F Series State Championship Series is perfect, 10 races and I’m fairly competitive in that series. Other dealers will be there on Saturday as well, including Compkart dealers.