Some information I found on CruiseCritic about taking the train from Cadiz to Seville:
Getting There: Easiest way is to take the train. From Cadiz, the station, just off the Plaza de Sevilla, is a 15 minute walk (basically on the other side of the port). Allow 1.5 - 1.75 hours for the journey between Cadiz and Seville and, for cruise travelers whose time in port is on the usual 8 a.m. - 6 p.m. schedule, the 9 a.m. or 10:05 a.m. (subject to change; check timetable at
www.renfe.es before you go) are the best bets. From Seville, there's a 1:58 and 3:25 p.m. return.
I checked the
www.renfe.es website, and assuming I used it correctly (no spanish understanding whatsoever). Looks like there is only 1 train to Seville on 4/20 in the morning leaving at 8:05 AM. It's cutting it close with a port docking time of 7:30 AM.
There are only 2 trips returning - departs Seville at either 12:50 or 6:58 (arrives in Cadiz at 8:44 PM).
These times don't seem to ideal to try and do Seville on our own. May need to reconsider other options then or staying in Cadiz.