Button Latch Circuit Not working in Real.Why

With the bottom switch open the gate of the N-ch FET is left floating and so vulnerable to any noise that may affect the circuit. If that noise brings the voltage at the gate high enough to conduct at all the N FET will form a voltage divider with the pull up for the P-ch FET. Since that pull up is a pretty high value at 100kOhms only a small current needs to flow to make the voltage at the P FET’s gate drop. A drop in that gate’s voltage will cause the P FET to start conducting letting the N FET’s Vgs rise even more and forming a positive feedback loop until both FETs are fully switched on. Shaking the circuit here to inject noise shows that: the LED can turn on without any switches being flipped because of noise. Making the P FET’s pull res a lower value like 10k helps make it more resilient against noise but leaving a FET’s gate floating will always leave it vulnerable to noise. I suspect the real circuit has some non ideal leakage currents somewhere and/or noise that kickoff that feedback loop and trigger the circuit even without any inputs.