What is the signal voltage (min/max) and what is the resistor value?
Seeing that you've already tried manual connections and assuming the signal is within safe operating range of the Arduino pin, you could try using an Arduino pin to programmatically control 3 states:
With the pin configured as an input, this would be your disconnected state (high impedance).
With the pin configured as an output, you could set it high (5V) or low (0V).
If the signal is compatible with PWM, you could have 256 different settings to dim the video.