Confused

In the simple on/off switched video, what is the power supply terminal 86 is going to if not the battery?

Which video are you referring to (is it in a webinar or in a course?) and a time stamp so I can take a quick look for you.

Assuming it's a relay, 86 is normally the +ve switching source - where the power to activate the relay comes from whether a switch or other power feed - and 85 being the ground for the solinoid.

In some applications 86 may be a 'permanent' live, such as from the ignition that is always powered when the engine is running, with 85 being a switched ground, like an oil pressure switch. Not seen so often nowadays, this was a common practice for powering fuel pumps back in the day - you may have noticed "Pumps Off!", above switches, in old race movies where the switches were manual bypasses of the pressure switch for starting, and the sign a reminder to turn them off so the pumps didn't keep running after a crash.

30 is the main power +ve feed to the relay and is usually from a fused source connected to the battery.

87 is connected to the device to be powered when relay is activated and, if applicable, 87a is the opposite of 87 in that it is on when the relay is off and off when the relay is on.