The firewall contacts are commonly corroded and so the drop there is not at all unusual. So, find some Packard 56 terminals and a good crimper for them; resist the temptation to just kluge in something. You probably have others in the same condition that need replacing. The ones carrying the alternator current into the dash area and also making the connection for the power to come in are very susceptible to burning up, as these carry by far the highest currents. The MAD bypass you may have rad about is all about bypassing those.
For some of the firewall contacts that are not corroded, a good cleaning will help. Apply some dielectric grease around the contacts when you are done and ready to assemble it.
As for the drop in the ignition switch, the current flowing through the blue wire is causing the voltage drop in the IGN1 position of the ignition switch. Basically, the plating is worn off of the ignition switch contacts internally, and there is resistance built up there. So, you should also go ahead and replace the ignition switch for sure. That is one likely culprit in the cut-out issue; a worn out switch is common. Easy to get at NAPA.
All the above is a 'pay me now or pay me later' proposition. So ignoring it is not a good idea.
As for the small can, based on the pink and yellow wire colors, look for an 'accessory connector and time delay' block on your FSM schematic. It think it is a relay for putting power onto things like...well actually I don't know what things! Look on the label to see if it says 'relay' anywhere. If it is, then it will be warm whenever the relay is active.
