IIRC, for 2003, the base caravans, without a tachometer, did not have the "eyebrow" above the instrument cluster. This "eyebrow" (or "Information Center" as it was labeled in previous generations), contains the high beam indicator and the left and right turn signal indicators, so these thre lights are not in the actual instrument cluster with a tachometer. So that would explain why the turn signal arrows did not work--they were not present in the instrument cluster.
I don't know for sure, but I think the 2003 models had a plastic panel in place of the eyebrow unit. In order to get these to work, you will have to add the eyebrow unit, and connect it up.
Or possibly, you could substitute an instrument cluster from a 2005 or later Caravan, Grand Caravan, or Town & Country. I don't know anything about whether the connections will fit.
In a 2006, this would not be an issue, because starting in 2005, the "eyebrow" has been eliminated, and all dash clusters have the turn signals and high beam indicators included.