I'd confirm by removing the ignition switch and letting it hang underneath the dash. Use a scerew driver to ensure the switch is in the off position. remember that ford's switch sequence is ACC, OFF, UNLOCK IGN, START. pulling switch up toward the steering wheel should get you to ACC position, one click forward is OFF. switch should have detents which make it somewhat easy to find each position. if the switch lacks detents, if it feels sloppy or mechanically messed up, i'd replace the switch just for peace of mind.
I 2nd checking other systems as well.
A failed voltage regulator on the alternator can also run a battery dead very fast, if it's shorted on. Dead giveaway would be if when running engine you see the battery go over voltage (over 14.99v) if problem persists, unplug the 3pin connector on the voltage regulator of alternator.
Stereo can also be culprit, if none the above works, pull the cigar lighter/stereo fuse.
Much less common, but If you have A/C, if the relay becomes stuck on, the electric A/C clutch can also run a battery dead fast. you could pull the A/C relay to test this theory, or disconnect the A/C clutch power connector. if you hear/see the A/C clutch disengage, well there's your issue. it should never be on with key off.
Using a test light between the battery terminal and connector to test flow may not be an ideal way of finding the issue, an LED test light will come on with very negligible current flow. if going the route of using testing tools between battery+ and connector, use a multimeter in 10A setting and wire in series to battery+ and the disconnected +battery connector. Do not turn ign on or run any significant load thru the multi-meter or attempt to start. the multimeter is fused and will not tolerate anything above 10A for a short duration of time. a nominal current draw of 50-100milliamps is normal. more than 100milliamps is a concern. if somethings running the battery dead overnight, it's likely in the 1000 milliamps or more threshold.
the fact you see no stereo on or indicator lamps on dash illuminated i believe means that the EEC relay is in fact switching off as it should. Pretty sure if that relay were stuck on you would see check-engine lamp and would find 12v at ignition coil and injectors.
Hope this helps.