I removed EVERYTHING on my friends truck, his is an 89 auto, and it worked fine.
Also the project truck that I have in my shop right now is an auto, and all is removed from that but I have not gotten into it yet to see what is working and what is not.
Always fun times going behind other peoples hacks.
All that I know that really needs to remain is the fat vacuum line at the rear of the intake, going to the modulator on the trans as @Axel-Breaker-Earl has said.
According to the Mazda Service manual here on this site, there are two types of auto transmissions
Electronic controlled
Hydraulic controlled
I guess I have never ran across one that was all electric yet as most are self working with only that vacumm line.
Then of course I think there is a kickdown switch on the gas pedal to make it drop down a gear when full throttle.
I am hesitant and excited to get into mine.