Squareback vs round back alternator?

Yes all points type ignitions must have the ballast resistor.
The resistor controls current through the coil keeping it from overheating. It also helps protect the points.
Only much newer systems, such HEI, have solid state control of coil current.

The resistor is bypassed during start because battery voltage is much reduced by the starter load.
During start battery voltage can drop between 9 and 11 Volts. That's why the key switch connects a second ignition terminal during start.

Alright, so I'll have to order a resistor as well and I'm thinking about changing the coil, spark plugs and cables and the condenser too. Like that it's all freshed up.
As for the resistor I cross checked the part number from the service manual: #1889545 which turns into #2196316 and this shows me this resistor:

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And this coil (#1688212)

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