My digital meter makes a buzzing sound when there is continuity, that's all I am going by.
Digimeters are STILL limited by their slow response time, even in the "buzzer" mode. Buy a $10 analog ohmmeter (or a suitable self-powered test light) to check your points-opening position.
The position of the piston is not important for this.
Well, kind of....You want the rubbing block of the point set you're setting to be on the highest part of the cam lobe. This is where you make your initial "rough" points gap setting for that point set. Timing comes afterwards.
it buzzes no matter if the points are open are closed.
You have a problem here. Either:
AA) the meter is not hooked up correctly or
BB) the point set has been installed incorrectly (grounded) or
CC) the condenser is shorted to ground
For AA) you have to be VERY careful with your probe to NOT touch the base plate (or any portion thereof) of the point set.
For BB) you may have an insulator washer on the wire attaching bolt of the point set in the wrong place.....or the little tubular insulator that fits around the bolt inside the points base plate is missing.
For CC) you need to disconnect the wire lead from the points first and then check the condenser from the lead to the condenser's casing with a suitable ohmmeter on the LOWEST setting. Make sure you touch the condenser lead wire to the casing to discharge the condenser BEFORE you attach your meter probes. If you get a low or zero resistance reading in this test, the condenser is shorted to ground internally and is history.
I'm supposed to put a probe where the lead attaches, right? And the other on the case or a ground?
Correct.....but this will ONLY work IF your points are installed correctly i.e. the wire and attaching bolt bits are installed properly. See above.
Does it matter if the ignition key is off or on?
Yes it does, IF you are using an ohmmeter (or buzzer), either analog or digital, or self powered test light. When using ANY ohmmeter on ANY circuit, that circuit MUST be non-powered (totally dead). Otherwise, POP goes the ohmmeter (or its fuse if it has one) and you let the "magic smoke" out of the meter. This, as we say in the biz, is a BAD THING.
Easiest way to be sure is to check the circuit with a voltmeter BEFORE starting to use your ohmmeter. That's why all properly designed meters have the voltage settings FIRST on the function selector knob BEFORE the ohmmeter settings.
So, after all this blather, the key must be OFF when checking points opening with an ohmmeter.