The fishing line isn't a bad idea, but it likely is not U.V. stable, and may degrade. Don't know exactly.
I did the same, and then changed out to an all vinyl twist-tie that came with some packaging, and I haven't lost my screen yet.
(about three years).
All good ideas...none that shouldn't be considered.
So long as you keep your screen...that's all that matters, eh?
Seriously, though....consider joining CoCoRaHS. They really need the volunteers, and the reporting is so easy and convenient.
Example:
Had to run to work this morning, and had no time to send my data.
I glanced at the gauge as I ran by....this time it was empty...no rain last night. Easy to remember.
But, I only made my data entry at 6:00PM when I got home from work. No worries!
As long as your observation is consistent, and it doesn't have to be to the split second each time every day...you're good to go.
Try it, man!
Plus, it will help you keep track if your electronic gauge is close.
So easy....don't let the commitment intimidate you.
Henry