Ok this is very complicated. Honestly I'm not sure. It's one thing to quit completely (and work at a pt job at another employer), it's another to quit ft work and came back on pt basis with the same employer. Typically, when someone's hours was cut from full time to part time basis, he is NOT eligible for EI benefits as there is no interruption of earning (no work & no pay for 7 days straight).
Again, the person in similar situation as yours, I think he also went back to his old employer after initial resignation. Each case is different so you may or may not get approved.