Does a Day Use pass allow entry/exits throughout the same day?

Yes

Yeap!

Park's Hours and Fees Fort Zachary Taylor Historic State Park Hours: The park is open from 8:00 a.m. until sundown, 365 days a year. The fort closes at 5:00 p.m. Fees: Admission Fees: $6.00* per vehicle. Limit 2-8 people per vehicle. $2.00* Pedestrians, bicyclists, extra passengers, passengers in vehicle with holder.