It is more than the "Widest" tire that fits. The wheels need to have the appropriate width associated with the tire. Wheel backspacing is another factor. The center section of the wheel needs to be properly positioned as the center of the wheel well and the outer end of the brake drum can be in different locations. This often requires an offset known as backspacing. There is also consideration of body roll in corner, as well as bump aspects in the vertical motion. Both can contribute to the tire rubbing on the wheel well, or wheel opening. And, if clearances are tight tire flex can also rub on the suspension.

That all said there are others here who have wide tires and can better get you close to an appropriate answer. Hopefully someone else will chime in.

Anyone know the widest tire that will fit under the rear of my 72 Runabout?

It depends on the wheels and backspacing, of course.  Now....that said, I'm running a 235/60 15 tire (Mickey Thompson ET Street Drag Radial) on a set of 7" wheels spaced for a Fox body Mustang.  However, I was just under the car with a tape measure and I think a 255/60 15 will fit on those same wheels.  If I had different wheels, or thought spacers were a good idea, I'm pretty sure I could get a 275 under it.  The limiting factor is distance between the inboard sidewall and the leaf spring.