You may have a first-generation "LSC"-type Pertronix unit, with a lobe-sensor sleeve on the points cam, rather than the magnet-wheel that attaches to the rotor. That particular Pertronix unit requires that the key be in the "on" position for 3-5 seconds to "charge" the module before turning the key to "start", but the previous owner failed to pass along that information (or the instructions). Turn the key to "on" when you get in the car, buckle your seat belt, then start it - that's enough time for the module to "charge up".
I tried your suggestion and the car does start easier but is still not right. I'm not sure this is a Pertronix unit - the lettering on the module is 33V-4V. I'm thinking I may have overheated the unit at one time. Maybe I left the key in the "on" position too long not realizing it could damage the electronics. Anyway, when I pulled the distributor cap, inside was what appeared to be the residue of an epoxy coating that possibly covers the electronics. Could this be and if so, what damage have I done to the unit?
This car runs like a scalded dog after it gets going. Sure wish the previous owner had advised me about the electronic ignition quirks though.