In this day and age, I can't believe ANY agent would not use email.
My training has taught me.. ask what method of communication works best for the client.. get the best phone number to reach them for both day/evening and use what THEY want. After all, the client holds your paycheck and you better earn it!
As others have noted, it seems like the agent you are working with is a part timer or truly doesn't know how to run his/her business, which is sad.
I spend bizarre amounts of time online, so it's not uncommon for me to respond to an email instantly or at 4am if I'm having trouble sleeping.
BTW, If you're looking in the Myrtle Beach area, let me know.. LOL..