I ended up having to attack this problem another way. None of the suggestions were able to successfully detect when the modalpopupextender was displayed. I instead changed my approach to handle user actions on the shown elements - like focusing on a textbox, etc. I could be confident the modalpopupextender was displayed if the user was interacting with it.
If you came here, I would direct you to the original post here - How to specify javascript to run when ModalPopupExtender is shown - and hope you were more successful than I was.
Thank you to everyone who commented, I sincerely appreciate your time.