I found out today that where you put the HTML for your modals could have an impact on how they function. Originally, I had the HTML for the modal boxes related to the first tab on my page contained within the content <div> for that first tab, and the HTML for the modal box triggered by a link in the second tab within that tab's content <div>. The modals for the first tab worked fine, but when I triggered the modal for the second tab the page dimming effect occurred but the modal box wouldn't appear.
I did some experimenting and discovered that if I moved the HTML for all of the modals outside of the markup that made up the tab interface, all of the modals would then work correctly.
Given that the modals were triggered by id-based jQuery selectors, I have no idea why having the modal HTML inside of the tab content made a difference. I can only assume it has something to do with how the content related to each tab is affected by the tab plugin.