Hmmm... Fair enough, if you're using the yellow composite connector, then it's not the connector causing that issue. It might be hard to find a bad cap in the video circuits without an oscilloscope (have you access to one?), but the only ones it could really be are C212 and C213, both near U12 (the video encoder). Pins 2, 3 and 4 of U12 are connected to pins 26, 25 and 27 of U30 (the video DAC) and carry the red, green and blue signals respectively. From your picture it appears that the green and blue signals are missing (25->3 and 27->4) whereas red is working (26->2). These signals are also used for the video out/monitor port on the A1200, and there are a couple of other components involved at that stage as well which might need to be checked.
But check for obvious things first: Look for short circuits around U30, U12 and the monitor connector, also around capacitors C211-213, diodes D231A-233B, and resistors R231A-232C... If it's not something obvious, you'll need to trace those signals with a scope to get a better idea of the problem...