74LS32 is a LSTTL series chip (really DTL). If you leave the inputs unconnected they are effectively at "1". You need to ground each input to get a "0".
Each input has a 20K typical pullup resistor.
I think you're going into far too much detail too early on. I've designed complex state machines many years ago and this kind of problem is going to be a bit tricky to get right.
Step 1, is to get the behaviour right. Don't even think about assigning binary numbers to represent the states yet. Clearly from your postings, you haven't really got the whole behaviour worked out.
Step 2 is assign state codes and go through the an implementation technique such as the algorithimic state machine method (ASM) to design and simplify the logic, assuming you are building a logic circuit to implement it. Then you can worry about physical implementation on chips such as field programmable logic sequencers (FLPS), or even FPGA's (field programmable gate arrays), and the representation of the design can either be as a schematic (schematic capture) or a hardware description language (HDL) based.
Don't worry about any of that yet. Just focus on designing the behaviour first.
You've gone straight into a state diagram. That's your end result. That's what you're trying to achieve, so you can then build the state machine.
I think you need to start thinking about using say, a UML sequence diagram to illustrate the behaviour. Each traffic light and sensor (inductive sensor) will be an object on the sequence diagram, and the sensors will trigger a set of behaviour, in a UML sequence diagram time flows down the page, so you can easily represent time based behaviour and what happens to the lights after the inductive sensor has been triggered.
So, I'd suggest design the time based behaviour using a sequence diagram first, then when you've got that right, got what you want, then you can move to a state diagram.
Then you can move to building it.
Best Answer
Your LDR when exposed to light changes its resistance which in combination with the potentiometer make a voltage-divider. This changes the voltage on the TR (trigger) pin of the NE555 and causes it to change its output.
The vibration sensor does not work this way, In your schematic you have shorted the output of the sensor to 12V line on BAT1. In your circuit remove the connection of RV1 to 12V and instead connect it to the output of the sensor.