OK! I figured it out.
Holy crap this was a slippery one to figure out.
The problem was that the team that was not showing up, although it had an agent in it, that agent was the only one in that team, and they were set to vacation mode. So because of that the team wouldn't show up in any of the assignment selections.
I had to dig though the source code and finally found the block of code that pulled the list of teams to display in the drop-down menu's. It had an array filter to hide any teams with no active agents in them. The team I had set up had one active agent, but she was in Vacation mode. The filter also doesn't count vacation agents when determining if there is at least one active agent.
TL: DR - Teams must have at least one active agent in them, AND if the team has just one agent, that agent cannot be in Vacation mode or the team is not displayed in the assignment selection.