The a/c operator demands an on time departure, its quicker to open them, have a quick look, drop them back down, besides, you're on your own and its tricky/dangerous to try and put the stays in on your own. You need to open them again in a minute anyway so you just leave them like that for now.
Exactly the kind of thing you need to avoid! That "for now" moment. Is the moment when you may be distracted. Best to not let that moment occur in the first place. It only takes 30sec to latch the cowls!
Each of those interrupts has differing levels of priority. Rather then the meanest or most friendly obtaining priority the jobs should be added to the engineer job list. Any direct tasking access to the engineer should be avoided, he should finish the job and associated checks then access his job-list to find the next highest priority job. Emergency interrupts to a job should be treated as the job being marked not-started so that there is no 'half finished' job.
I agree Ian
I recently had a dispatcher carry a tech log across from another aircraft, whilst I was changing a brake unit.
"I only need a quick signature"! He said.
"
"
He soon went off with his tail between his legs!