Pathfinding to have a character follow at a former location is a bit overkill and can take up quite a lot of CPU resources.
You referred to snake. Originally, snake is a grid movement.
It keeps all the locations of your characters (members) in an array.
Each "tick" you update the position of the main character/head and position the next element of the body to the former position of the previous element.
You pass this way through all the elements of body, position them accordingly and save each of their current position in the array.
The next tick, you do the same.
Depending on what movement system you are doing you can adapt it and do the same in Construct.
Or otherwise, you can also Pin Behavior (set to "position" using a rope style) and pin the characters to one another, making a "chain" that is being pulled by the main/first character.