We have setup a solar stairwell project at home, using LED and salvaged batteries and this is what it looks like:
[![enter image description here](https://i.stack.imgur.com/k1Qn3.jpg)](https://i.stack.imgur.com/k1Qn3.jpg)

However it may look, the circuit can be oversimplified to:

![schematic](https://i.stack.imgur.com/nysJk.png)

[simulate this circuit](/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2fnysJk.png) – Schematic created using [CircuitLab](https://www.circuitlab.com/)

i.e., it's a battery at the top of my house, ( which is charged using solar power ) and all the LEDs run to the bottom of the house with all of them staying in a parallel configuration.

As you might have guessed, we did not have sufficient brightness at the end of the stairwell. The voltage at the bottom of the stairwell is around 8V. So, when we found another salvageable battery yesterday, we connected it to the stairwell, and it worked well.

The new circuit would look something like this:

![schematic](https://i.stack.imgur.com/Y9MUt.png)

[simulate this circuit](/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2fY9MUt.png)

However, we wanted to operate the whole stairwell using only a single switch, so I came up with an idea of using a relay to turn on the 2nd battery downstairs but I can't think of anyway to turn it off using the same switch upstairs, as it is creating a sort of feedback loop.

![schematic](https://i.stack.imgur.com/QX3zj.png)

[simulate this circuit](/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2fQX3zj.png)

I used a 5V relay at the yellow wires as it was the only thing lying around in my house. I'm fairly certain that the blue section is causing a feedback loop, but I've already spent a whole night to think of way to solve it.

Both the batteries are heavy, so I cannot move them, they must remain upstairs and downstairs as I don't want to clog my stairwell. Since it's a stairwell, I can only add very minimal circuit in the middle as it's very difficult to work there, but if it's impossible to do so without tampering in the middle, I would live with it.

Apologies for the verbosity of my question, I'm pretty sure that someone from the industry might have faced this problem before and have a solution at hand. I'm just an enthusiast with no proper industry training and couldn't search for this problem precisely online.

All help would be appreciated.