How to cancel out only first High signal while receiving to remaining ones
You can build logical AND gate with transistors:



Where the A signal would be connected to your motion sensor, and B signal would be connected to RC charged capacitor. Imagine capacitor that is initially discharged. After turning the device on, through a big resistor it starts charging, until it reaches some voltage required the transistor to turn on. Try with values R=100k, C=100uF, or calculate the time constant precisely. Dont forget to put some huge resistor in parallel with C, so after turning the device off, it will fully discharge the capacitor.



Simulate the scheme in falstad. I had to move the resistor from emittor to the collector, so it produces negated output (NAND), with third transistor we invert it back to get AND gate. The simulation in falstad is quite slow, so I set the pulse generator to 20 Hz and also reduced the capacity 10x. From the simulation you can see that when the capacitor reaches about 0.7V, it opens the transistor on bottom, the second transistor is triggered by signal generator (motion sensor)