Squeegee for lower back window

I live in northeastern U.S. and get a lot of dirt and mud on the lower back window, especially in winter. I have a long, dirt driveway.

My game plan is to pour some window washer into a spray-pump bottle and buy a 6" squeegee (like the kind they have at gas stations, only with a narrower blade) to keep in the car throughout the winter.

Anyone have a better suggestion?

If this seems like a good plan, any suggestions for where I might find a 6" squeegee?

I wish I could flick a switch from inside the car to squirt windshield fluid and run a back wiper horizontally along that window.

I struggle with backing up in the Prius even when everything is clear. Having the lower window in play is very helpful. (Part of the problem is also keeping the camera lens clean and dry. There always seems to be a drop of water on the lens, distorting everything).

Thank you,

Mary