By the time I'm out of observation it'll have been over 4 hours to get vaccinated.
Some tips
Carry a small umbrella. If a hospital has supplies there will be long lines. Mostly on the road or in unsheltered compounds. It's hot. I reached before 9 and stood in line till noon.
Carry a water bottle. Maybe even a sandwich or some dry fruit if you have senior citizens with you.
Many hospitals are providing wheelchairs for the aged but obviously in limited quantity.
Light clothing, face wipes, hand sanitizer will help you keep your sanity in the sun.
I had to visit two hospitals before a family friend alerted that the hospital she was in had vaccine supplies.
So network with friends and family as the supply situation is very fluid.