Checklists are tough. To a great employee, they feel like a waste of time, big brother intruding and micromanaging. To a bad employee, they are marginally effective. I think your better off creating an install kit for each employee with basic tools and make them responsible for it. I suggest at least 2 each of the inexpensive tools like squeegees, knives, extra blades, tape... It is quicker and cheaper to grab the spare than spend 5 or 10 minutes looking for a tool. That's 5 or 10 dollars in billable time wasted looking for an inexpensive tool.
All the major tools stay with the vehicle, like ladders, drills, levels, a basic hardware selection, and spare essential tools. Each shop will have a different workflow and tool requirement. Make sure they understand that if they use a spare they need to replace it or it won't be there the next time.
After that, it becomes a management problem. Have a quick meeting before they load up and discuss any special tools that may be required. Many times the installers are going without ever seeing the site and may not know what is required. A daily, weekly, then periodic reminders help until it becomes a habit.
Try and simplify your requirements down to the basics. I used to use lists to track VIN's, Tag #s, and Unit #s. It was too time-consuming and installers are usually battling the clock and trying to get home at a reasonable time because they are the last in line. They have to deal with all the problems that weren't addressed in sales, design, and production. Now I take a picture of the VIN and any damage that may come back on me. When completed 8 pictures of the vehicle. One from each side and corner which will include the Tag and Unit numbers. With the VIN first on each vehicle, it's a place holder between each vehicle. If they need to be written down, let someone in the office do it instead of texting all day.
Once you have established a clear policy/requirements, hold the bad ones accountable and reward the good ones. At one shop I worked at the boss paid $10 per job that went without a hiccup and it reduced the problems enough to pay for itself.
And remember, all of us make mistakes from time to time. it is the consistent offenders that are the problem.
P.S. One thing I learned from my first boss was to walk around the vehicle and double-check for trash and tools before you leave. A couple of minutes a job will save you $ in the long run. " I can't find my V-Cat, RollePro, magnets...