According to my definition, the switch can only be operated from 'below'. After that, the move N c5-A4 would not be possible.
A switch is an overlapping pair of spaces that in some ways operate together as a single space. By their very nature, they operate as a switch only from a given direction. From below, a piece is given two choices for how to continue its vertical movement. However, this property of a switch is not a property of the individual spaces whose overlap constitutes the switch. So, restrictions on movement to A4 have nothing to do with your definition of a switch. They are simply arbitrary restrictions on movement.
There are already other examples of A4 being reachable from above. For example, a Rook or Queen on a8 could move to A4, and a Bishop or Queen on e8 could move diagonally to A4. You have also agreed that it makes sense to let it be reachable from the side.
I'm now going to propose some rule changes. Since the switch can make a piece more powerful, this should be balanced by making a piece using a switch more vulnerable. Allow pieces access to the spaces of a switch from any direction, and when a piece moves to a switch, allow capture of any piece on the switch even if the capturing piece moves to the other space. For example, if a Bishop is on A4, and a Rook moves to a4, consider the Bishop on A4 to be captured.
Currently, the Knight is the only piece whose powers of movement are restricted in the vicinity of a switch. Correct this by allowing a Knight to move to any space that can be reached by a step in an orthogonal direction followed by a step in an outward diagonal direction, or by a step in a diagonal direction followed by a step in an outward orthogonal direction. This is the normal definition for how a Knight moves in Chess and other variants, and it would allow the Knight to also increase its capabilities in the vicinity of a switch.
One last rule change I would suggest is to let Rooks, Queens, and Kings use their ability to move horizontally to switch between the spaces constituting the switch. This would basically involve lifting one more restriction on movement to the spaces making up a switch.
A switch is an overlapping pair of spaces that in some ways operate together as a single space. By their very nature, they operate as a switch only from a given direction. From below, a piece is given two choices for how to continue its vertical movement. However, this property of a switch is not a property of the individual spaces whose overlap constitutes the switch. So, restrictions on movement to A4 have nothing to do with your definition of a switch. They are simply arbitrary restrictions on movement.
There are already other examples of A4 being reachable from above. For example, a Rook or Queen on a8 could move to A4, and a Bishop or Queen on e8 could move diagonally to A4. You have also agreed that it makes sense to let it be reachable from the side.
I'm now going to propose some rule changes. Since the switch can make a piece more powerful, this should be balanced by making a piece using a switch more vulnerable. Allow pieces access to the spaces of a switch from any direction, and when a piece moves to a switch, allow capture of any piece on the switch even if the capturing piece moves to the other space. For example, if a Bishop is on A4, and a Rook moves to a4, consider the Bishop on A4 to be captured.
Currently, the Knight is the only piece whose powers of movement are restricted in the vicinity of a switch. Correct this by allowing a Knight to move to any space that can be reached by a step in an orthogonal direction followed by a step in an outward diagonal direction, or by a step in a diagonal direction followed by a step in an outward orthogonal direction. This is the normal definition for how a Knight moves in Chess and other variants, and it would allow the Knight to also increase its capabilities in the vicinity of a switch.
One last rule change I would suggest is to let Rooks, Queens, and Kings use their ability to move horizontally to switch between the spaces constituting the switch. This would basically involve lifting one more restriction on movement to the spaces making up a switch.