Here's how I solved the radio problem in my 2a.
I ran a wire from the permanent live fuse, through a switch and spliced it onto the radios' +ve feed, the one that runs from the ignition.
And most importantly, I cut the +ve feed (from the ignition) wire & put a diode in-line to prevent current running back through to the rest of the loom.
Like everyone else has commented, if you leave the ignition on without the engine running the coil will heat up alarmingly, without the constant circuit breaking from the distributor it's just a coil of wire, same as a light bulb or old fashioned 3 bar electric fire.
Here's a pic of the roof console I built for the radio.
