It's not an additional signaling.
TVs were designed in the 30's, where electronics were extremely primitive and expensive. You wanted the consumer device to be as simple as possible so it could be within the consumer price range. So TVs were little more than a Radio receiver hooked up to a cathode ray tube (CRT).
To drive a CRT you need 3 signals: X position, Y position and brightness. The dumbest possible design is to have 3 radio receivers and transmit all 3 signals over the air. But the extra receivers are expensive and besides the X and Y signals are very repetitive, which would be a waste of bandwidth.
So two flyback transformers were added to the design of the TV, which generate a saw wave pattern. Starting at 0% they would consistently increase power until 100% before rapidly snapping back to 0. One would run at the vertical refresh rate to drive the CRT's Y signal and the other would run at the horizontal refresh rate to drive the CRT's X signal. The Brightness would come from the radio receiver.
With this design, you just need a way of synchronizing the TV studio's cameras and all the TVs in the area to the same horizontal and vertical refresh rates. You might think: Easy, we just use the mains power frequency for vertical and then divide it by 525 to get the horizontal frequency.
But a 525 frequency divider way too expensive to put in every TV. Instead, they only put one divider in the studio to calculate the horizontal refresh rate and transmit a synchronization pulse embedded into the brightness signal. A simple circuit in the TV detects the synchronization pulse and nudges the flyback transformer to match. A second, longer synchronization pulse is transmitted between every field for the TV to synchronize the vertical flyback transformer.
So a basic Black and White TV is just a radio receiver, two flyback transformers and two synchronization detectors hooked up to a CRT. It doesn't know anything about interlacing or even how many lines there should be in every frame. Back then, a TV studio could theoretically start transmitting at 61 Hz or with a few extra lines per frame and every TV would follow along, right up until the point where the horizontal or vertical refresh rates went out of the spec of the shittest flyback transformers in consumer TVs.
Interlacing is a brilliant hack that is 100% done at the studio end. All they do is pick a horizontal and vertical refresh rate that don't divide into each other a whole number of times. 60 hz divided by 15.750 kHz is 262.5 lines. This means that when the TV's vertical flyback transformer reverts to zero (putting the CRT's Y position back to zero), every second frame, the X position of the CRT will be halfway along the screen.
One thing you might have noticed is that the Y position is constantly incrementing, it doesn't step down by one line worth of y position at the end of each line. This means that the TV signal is actually rotated slightly, with the end of each line having almost the same Y position as the start of the next line.
Which means if the field starts halfway through a line, the start of the first full line on that field (and every line after that) will be half a line lower than it was on the previous field.
Other interlacing schemes are theoretically possible, just by picking appropriate horizontal and vertical refresh rates. You could have Triple interlacing or quadruple interlacing (though I doubt either would be pleasing to look at). But most early game consoles and computers pick a horizontal and vertical refresh rate which divide into each other with a whole number of lines, resulting in a progressive display.