How do you get in touch with these people over the phone to make reservations? Nobody seems to answer the phone

Go online and search Tim's ford state park and you should get phone numbers. Keep trying back.

931-968-0995 Park Office May 1 to October 31 9 a.m. – 5 p.m. Sunday- Thursday 9 a.m. – 6 p.m. Friday and Saturday

Tims Ford State Park — Tennessee State Parks "Tims Ford State Park — Tennessee State Parks" https://tnstateparks.com/parks/tims-ford