The base is an "ON STAGE" LED sign powered by 2x AA 1.5V batteries. The connection of the LED sign has to be changed, so it matches to the following schematic:

Connect to the HM-10 module via serial converter with 9600,8,N,1. (some configurations are 115200 baud)
Sending AT+VERS? or AT+VERR? should generate the answer HMSoft V540. If not, the firmware has to be updated.
As next the module has to be changed to be accessed by BLE:
AT+MODE1 // makes it possible to receive AT commands via BLE
AT+PWRM0 // Activates 0.4 mA unconnected, 8 mA connected
The software will send following commands:
AT+PIO20 // turn off the PIO2 GPIO, so LED will turned off
AT+PIO21 // turn on the PIO2 GPIO, so LED will turned on
The project is using some BLE routines of https://github.com/jnross/Bluetility for the Swift BleOnStageLib
See also a good tutorial on HM-10 at following webpage: http://esp32-server.de/hm-10/
