Sako wrote: hey!
how do I identify if the hall effect sensor design is a pull up or a pull down?
You can look at the voltage on the signal wire which will be either 0v or something like 5v or 12v. Then unplug the connector from the sensor and see if there is a change in voltage. If it goes from 0v to something like 5 or 12, then it's pull down. The other way around would be pull up.
In the first example, being pull down, you could then act like the computer by putting a test light to ground and tapping on the signal wire. That should pull the voltage down, indicating good wiring. Even a rise from 0 to something else would indicate good wiring.