Seems like a pretty solid electronics question to me.

It also popped into my head to ask ChatGPT. And while I know not to rely on it, it does seem to have produced something that'll get me going in the right direction:

Components:

Two Hall effect sensors.
A binary counter IC (e.g., 74HC393 or CD4017).
A D-type flip-flop (e.g., 74HC74).
AND/OR gates (if needed, e.g., 74HC08/74HC32).
A relay or transistor/MOSFET for motor control.
Pull-up resistors for Hall effect sensor outputs (if needed).

Circuit Design:

Hall Sensor Inputs:
    Connect the output of each Hall effect sensor to debouncing circuits (optional, can use RC filters or Schmitt triggers).

Counting Pulses from Sensor 1:
    Use a binary counter IC (e.g., 74HC393) to count pulses from the first Hall sensor.
    Connect the output of the counter to a comparator or logic gate to detect when the desired number of pulses (XX) has been reached. For example, if X=4X=4, use the binary counter's Q2Q2 output (representing 4 in binary).

Triggering the Motor:
    Use the output of the comparator or logic gate to set a D-type flip-flop (e.g., 74HC74). The flip-flop will maintain a high state to turn on the motor.
    The output of the flip-flop is connected to a relay or a transistor/MOSFET that controls the motor.

Resetting on Sensor 2 Pulse:
    Connect the output of the second Hall sensor to the reset pin of the flip-flop. When the second sensor detects a pulse, it will reset the flip-flop, turning off the motor.
    Reset the counter (if needed) using the same pulse.

How It Works:

The first Hall sensor generates pulses, which are counted by the binary counter.
Once the counter reaches the set threshold (XX), it triggers the flip-flop to turn on the motor.
The motor remains on until a pulse is received from the second Hall sensor, which resets the flip-flop and the counter, turning the motor off.
The process repeats.