This is the OEM VDO tach and when everything is off, it reads zero.
When the ignition is turned on (lately) it goes to 1000 rpm. At idle
it reads maybe 12-1500 which is faster than it has been idling.

Before, it did like it was supposed to, reading zero when the engine was
stopped (with ignition turned on), pulsing a bit with cranking and then
reading 800 at idle and higher during operation, apparently correct.

Now, with ignition off, it reads zero. With ignition on, even with the
wire to the distributor disconnected (or connected) it reads 1000.
As I mentioned before the tach in my 73 164 did the same thing. Gotta be
something in the power supply or internal circuitry if it does it with no
signal input.