i just checked two different styles of rims... one was 1.7mm thick at the bead seat, the other was 1.87mm thick at the bead seat... both are in new condition, with no wear...
depending on how the brake pads were aligned on your bike, you may be riding on .020" of material or less...!!!!! that's 1/2 mm, btw...

there are no proven, set in stone, rules for rim wear.... when the rim's outer lip separates from the rest of the rim, the tube will most likely blow out suddenly.... ouch! you may get a warning in the form of an odd pulsing in the brakes on that rim.... it will fail while cornering, most likely.... or while under hard braking...

i've caught more than a few worn rims before they failed completely... the owners bring the bikes in for wheel truings usually... the rims get weak before failure.