... Any way to accurately test that it works without specific equipment? ...
Not really. These things were routinely replaced, bad or not, along with the points and the distributor rotor because (1) it is easy to do so and (2) if it is bad it would save time not having to remove the distributor cap again. Those particular capacitors are damned reliable because they have to be, considering where they are located under the distributor cap and right next to the cam and ignition-coil switch-points. That's a very hot environment after the engine has been running for awhile.
Most of them fail from excessive leakage, rarely by outright shorting, although that is a typical failure mode for capacitors. To test leakage, you need a power supply, a sensitive current meter, and a current-limiting resistor (in case the capacitor is shorted) all connected in series with the capacitor. There should be at most a few microamperes of leakage with a hundred volts or so applied with the power supply. Ideally, there would be zero measurable leakage current, but hey! This is the real world. These capacitors absorb and release amperes of current when operating. A few microamperes of leakage won't hurt anything.
The voltage "spike" that occurs in the
primary of the ignition coil when the points open (collapsing the magnetic field in the ignition coil and creating a high voltage in the secondary winding connected to the center post of the distributor) must be suppressed (absorbed) by the capacitor for proper operation of the coil and preservation of the point contacts. Without the capacitor connected, this "back EMF" created in the
primary can reach hundreds of volts and cause serious arcing and erosion of the points as well as timing problems.
The best "test" that I know of is "if it works don't fix it." But most mechanics usually do, replacing a good capacitor with a who-knows-what capacitor, imported from a who-knows-where country, with unknown quality control. Keep the old one as a spare in case the replacement prematurely fails. The old one will probably work just fine.
