If the beacon is powered from the receiver, cutting its power supply will certainly stop it switching on. Ever.
A link to it might help with guesswork, but the fact that stick movements do turn it off suggests that it expects something on the signal wire. As a temporary test, winkle out the brown wire and see what happens. This will stop the signal but let the beacon draw power. If it wakes up in the required mode, job done.
Black/orange/brown is unusual, but the usual arrangement is that black is nearest the edge of the TX board and is -ve power, the center pin is +ve, and the other one is signal, whatever the colour scheme.