Fooling RCA cable into thinking it's connected
NOTE: This was a project to see how inexpensively I can hook up a dash cam. The camera itself was very inexpensive, and I did not mind damaging it in the search for the cheapest solution. Caveat emptor!

THE ANSWER: Before investing in a resistor (see discussion in comments of my question), I tried the simple expedient of shorting the jack out with a piece of foil. I figured that the risk was low as I read elsewhere that RCA video has low voltage and current. This worked! The camera no longer shuts off automatically.