Any chance you have a loose wire and with the coil upside down the coil feed wire (from the ignition switch source) wire is pulled away from the terminal?

And when the coil is returned to upright the loose wire returns to the contact where - even though loose - it transmits electricity.

You could prove or disprove this theory by running a jumper wire from battery positive to coil positive (ignition switch side of the coil).

If things start working then you can check the wiring for problems.

I've seen coils mounted upside down now and then.
The owners didn't report any problems.

I also note that more than a few factory stock cars have the coils lying on their sides.