They don't post wait times at the entrance but you can check the park webcams to get a feel for the length of the line. The parking lots do not have webcams but the lots by the Visitors Center are sprawling and in multiple directions. The overlooks to the east of the VC do not have shuttles so usually people are leaving to view those and spots open up. It isn't like Zion where it is the only place to park and you are required to use a shuttle. You can usually find something even on busy days but it may not be in the first row.

Thank you for the information dbmove.