You definitely should be able to breathe. There's good info on this stuff on the partial hanging thread. If you wrap your hand around your neck right above the adams apple (if you're male), you should be able to find a spot on each side with a pulse. That's where you want the pressure going. Just keep messing around with the positioning of your hand until you find the pulses. Apply some pressure with your hands briefly to see if you start feeling lightheaded etc. You should be able to breathe but feel yourself passing out. I'm still trying to do it myself, but it's been SI stopping me. I feel I've found the right spot, but it's been taking longer to pass out than I've heard, which always leaves me too much time to bitch out.
One thing I've considered is somewhat combining the "night night" method with partial. Put something in between the rope and my carotid arteries so that more pressure is applied there. It makes sense in theory, but I'd have to find some other stories of that being a viable method.
Either way hope this was at least a bit helpful. Sorry you've reached this point too.
