Using a Servo Pulse to Initiate a Sequence

I am new to Arduino and own an Arduino Mega. Ive built and R2D2 and recently received a lifting mechanism from another builder in our group. On the lifter board there is a pin that needs to be connected to 1 of 3 other pins on the board in order to complete a calibration and then put the board into a demo mode. By hand you would need to take the wire connected to a Ground Pin on one side and connect it to Pin A to run a vertical calibration, then remove it from Pin A and move it to Pin B to perform a rotary calibration. Once the two calibrations are satisfied I can then move the connection off of Pin B on to Pin C which will cause it to go into a demo mode of random ups and downs with rotations. When I want to come out of Demo mode, i would remove the connection from Pin C and move it back to Pin B to allow the system to find the Rotation center and retract the lifter back to its home position.

From an arduino stand point, I have no idea where to start. I need be able to put the arduino between the ground Pin connection and the ABC pins as well as receive a Servo pulse from a receiver. The code in the arduino would need to be able to identify the pulse and perform the Pin A connection for X seconds, Pin B for X Seconds and Pin C for X seconds, then Pin B again.

Any suggestions on where to start?

You need to know whether any appreciable current flows into or out of pins A, B or C when you connect the GND wire to them.

You also need to know what voltage is on the pins when they are open circuit (i.e. voltage from pin to GND when the pin is NOT connected to GND).

If the current flow is less than 20 milliamps AND if the max voltage does not exceed 5 volts you may be able to use an Arduino OUTPUT pin to pull the pins to GND.

If the voltage OR current is outside those limits you may need to use relays between the Arduino and the device so that the Arduino is not damaged. Possibly a simple transistor triggered by the Arduino would be sufficient. You will need the transistor in any case if you use an electro-mechanical relay because the Arduino I/O pins cannot provide enough current for the coil.

I don't understand how the servo pulse relates to all this. What is producing the pulses?

...R

Simple transistor/relay circuit to switch a signal between 1 of 3 places.
Can use 5v Telecon relays if low current:

The Arduino would be connected to a remote control receiver with Servo outputs. Basically when I toggle a switch on my remote, it would send a signal to the Arduino to perform the action. As for the voltage and amperage between the ground and the ABC Pins I am checking with the designer of the board. I want to say that its very minimal.