Welcome to the forum. Just thinking, a Fiat 126 must be a rare car in the USA!
If you have to disconnect the battery to get the engine to stop then I don't think this is 'dieseling'. On a petrol (gasoline) engine, 'dieseling' is usually caused by little bits of carbon in the combustion chambers glowing red-hot and igniting the incoming fuel-air charge thereby causing the engine to 'run-on' (usually roughly) even when the ignition is turned off.
It sounds to me that there is still a live feed (power) to the ignition coil with the ignition switch turned off. To check this, put a voltmeter or test lamp between the low tension side of the coil (+ or B) and earth (ground).
There should be no voltage/lamp unlit with the ignition off and approx. 12volts/lamp lit with the ignition on.
Or,next time the engine won't stop when the ignition is switched off, try disconnecting the wire to the coil + or B terminal. Or pull the coil HT (king) lead out of the coil tower. Or earth (connect to ground) the contact breaker side (-ve) of the coil. You can do this most easily at the low tension connection on the side of the distributor with a screwdriver or a short length of cable.
Could be a faulty ignition switch or someone has been playing with the wiring. Any accessories such as engine immobiliser, alarm, remote start etc. fitted?
Something else could be providing an alternative power supply to the ignition coil independent of the ignition switch.
P.S. If your 126 is fitted with an alternator, I don't think it's a good idea to disconnect the battery with the engine running, might cause some damage iirc.
Al.
