Data will travel at the speed of light within a margin of error, so "a few light seconds" means "a few seconds".
There will be some lag as each satellite would need to cache the data before retransmitting, and it would need to store that data for a short period as well in case of failure, so assume that it would double the time for each stop under ideal locations, so to get information 4 light seconds away would take approx 8 seconds, and a minimum of 16 seconds for a response assuming they started replying the instant they received.
There will be some lag as each satellite would need to cache the data before retransmitting, and it would need to store that data for a short period as well in case of failure, so assume that it would double the time for each stop under ideal locations, so to get information 4 light seconds away would take approx 8 seconds, and a minimum of 16 seconds for a response assuming they started replying the instant they received.