Agents are pretty much useless for esoteric stuff. VS website makes it clear that TPA lounge is 3rd party lounge called "International Club Lounge" near gate 78 (AA lounge is near gate 85). You can see them on the map from Tampa airport website. While not an actual VS Clubhouse, they mention that VS Gold cardholders have access to this lounge in addition to Upper Class. So they might let in DL GM+ members in as well. But I wouldn't necessarily count on that. Anyone who doesn't have VS/DL Gold+ or isn't flying Upper Class is almost certainly not going to get access.