So which resistors will I need? To produce a white signal, the sync and video lines will be high. The equivalent circuit looks like this:
(The 75Ω resistor is the resistance inside the TV).
To show a black signal, the sync line will be high, and the video line will be low, which looks like this:
Wikipedia gives the formula for a voltage divider, so the resistors in the first diagram can be calculated with this formula:
and in the second:
I tried solving these, but that’s well beyond my mathematical ability. Instead I found some online site that could plot the two formulas (edit: I could have used Wolfram Alpha). The lines crossed at about RV=250Ω and RS=580Ω. These resistor values don’t exist, so RV=270Ω and RS=560Ω is close enough. They seem to work fine in the circuit.