I'm not that intimately familiar with the '73 1800 (I did have a '73 164, though) to know whether the light is also tied in with the handbrake on switch, or not.

But if you've eliminated that possibility, and you're left with the "octopus" (pop name for the many brake lines that converge in the device that compares brake fluid pressure in the two triangular brake circuits, as "Dave B" already described), then besides the idea that the pin has been dislodged from the middle by a brake fluid leak or flush (which sometimes happens) you can also consider that the switch is just corroded and shorting out -- remember that it functions by "grounding" the warning light's circuit.

A while ago (many years back) my warning light came on, too (though it was on my 240, not an 1800). It certainly wasn't because of any imbalance in brake line pressures, but happened to be because the switch, so old, just had corroded and shorted out to ground. I got a switch rebuild kit from Volvo and simply screwed out the old switch (literally falling in pieces) and screwed in the replacement. I didn't have to disconnect the "octopus" or its brake lines -- I worked with it while it was still bolted in place by crawling under the car (on jackstands) and working with a small mirror and tweezers (the job has to be done upside down), but it was easy.

I doubt the rebuild switch kit would be the same as on your 1800, but the kit for my 240 was p/n 272702-2 ($36.23), so maybe this will help your dealer's parts guy find your part.

Good luck.