My old elementary school had toggle switches throughout the hallways that were in the middle position (between the "on" and "off" positions. The switches had no markings on them and some had the Circle F logo on the front of the toggle. Does anyone know why they were in the middle position?

They might have been an early version of low voltage relay switches. They could have been by default in the middle position, and to turn on, you pushed up against a spring to make a momentary contact with the on circuit, and the same for the off circuit in the down position. More typical installations use the same principle only with rocker switches that are kept in the middle position.

They might have been an early version of low voltage relay switches. They could have been by default in the middle position, and to turn on, you pushed up against a spring to make a momentary contact with the on circuit, and the same for the off circuit in the down position. More typical installations use the same principle only with rocker switches that are kept in the middle position.

I think they are maintained contact switches. Once, when I was in first grade, one of my classmates flipped one of the switches to the up position and it stayed there. Some of the lights also turned off when the switch was up. Also, that place had small sideways rocker switches that made momentary contact.  I later found out that these rocker switches were used as low voltage relay controlled lighting.

Do you think this could have been a way to control multiple lighting circuits with a single switch and without using a duplex switch?

With relay control many schemes are possible, like master on / master off etc

In my high school old building (built 1980) the lighting was controlled by ordinary 3 ways. If you did it on the switch in the far end of the corridor, no one will be able to switch on the light from the other switch

In the newer buildings of high school (built 1987 and 1992) and in elementary (1995) the control was by step relays. On the wall is an ordinary momentary push button, you click it to switch the light on or off. You could hear the relay clicking in and out in the electrical cabinet when you press and release the button

My church has these switches in the middle position for the lights, but normal (up for on, down for off) for the fans. The lights have down downlighters (with R30 lamps) and lights with diffusers (with normal A shape lamps) both controlled separately. I think these switches can control multiple loads in a single switch (where down is off, middle is both on, and top is one load). Sometimes, the downlighters are off with the other lights on.