If you put a voltmeter across the points, what you will actually measure is dwell: if the points are open half the time, then the reading will be half of the ignition voltage. If the points are open one-third of the time, you will read one third of the ignition voltage, and so on. Tachs use a capacitor in series between the points and the meter, and a diode across the meter. When the points open, the voltage rises, and the capacitor "dumps" its charge through the meter. When the points close, the diode refills the capacitor. The more rpm, the more of these pulses from the capacitor and the higher the tachometer reading.
You are lucky to have points. My diesels have tachs running off of the alternators. This is a pain to calibrate, and if the belt slips the reading is too low - not a good thing.
Most automotive gauges will stay where they are when the ignition is turned off. But some return all the way left (below zero). I assume that these have a small spring, or the armature is weighted so that gravity brings them back. Perhaps this is so they will look "off" when there is no ignition power.
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida