Easiest Method if you have numlock keyboard with 4 and 6 as directions. (Credits to Volomon and legitplayerislegit for mentioning and displaying the method)
Step one - press numlock (auto run)
Step two - Press 4 or 6 and dont let go of the button
Step three - While still pressing 4, press numlock again to stop auto run (you will continue to circle on the same spot)
Step four - Let go of 4 (now is auto rotating) and press numlock to auto run.
So there are many methods to do this, here is the way i use:
First you need to make your game into window mode (not fullmode), Then ride your pet and hit that autorun key (mine is numlock), press "a" or "d" key to go whichever direction you want. Now comes the important part: while still holding either direction key right click at the top bar of the game, a drop down menu bar should open with info such as : restore, move, close ect. Let go of the key you were pressing and wala, you are not auto running without any 3rd party software or jamming your key buttons.
Bonus: Mute archeage, put it almost all the way to the side but enough where you can rightclick, open your series or movie on window mode covering the screen till the tip of archeage, then press archeage and autorun + direction key, right click, letgo and enjoy your movie as your mount gets leveled up.
Warning: if you press outside archeage or it is not selected highlighted then your character will just be autorunning without circling.
Note: if you stopped auto run but your screen is moving round and round, just click outside the game and it will restore it back.
Enjoy