You never release the park brake until you see the engineers walk away and wave you off with the pin....EVER.
You never increase thrust on an Engine above idle without Engineer approval on the headset AND ATC clearance.....EVER.
Lessons learned the hard way before this incident killed someone, it should NOT have happened.
In some places if you are trying to be clever and request taxi clearance before the Engineers are clear ATC will tell you the engineers are still under the nose, why are you requesting taxi now? I've heard it plenty of times....