Home E / extrude until endstop is triggered
You should be able to adapt the "Dual X Carriage" feature for your project.

That allows a second print head (on the X axis) to move independently of the "main" X axis motor - and it can also be homed against its own endstop.

You can enable this feature in the configuration_adv.h file under "Dual X Carriage".

By default, all "Dual X/Y/Z axis" features use the first free extruder stepper driver - which would be E1 in your case.

You would have to adjust the X2 parameters to allow you to zero the motor on the endstop (X2_MIN_POS 0, X2_HOME_DIR -1, X2_HOME_POS X2_MIN_POS), as well as setting the default mode to "FULL CONTROL" (DEFAULT_DUAL_X_CARRIAGE_MODE DXC_FULL_CONTROL_MODE).

As far as I understand, you can then use
T0 and T1 to change between both "X axes", with T0 selecting your real X axis, and T1 your custom stepper motor.