Through trial and error, the '/hotbar' macro type appears limited to using numerical conditions. However, the '/hud' type allows for typed elements like 'Duty List', etc.

Try:

/hud "Pet Hotbar" off

in your macro. It worked for me

P.S. for positional changes in the location of the pet hotbar element based on job, you may want to copy your existing HUD layout to any other available HUD profile (you should have three additional); move the desired element(s) in that alternate HUD profile; create a job change macro that switches any pet-based job to that HUD profile.