A simple idea would be to mask off an arc that the windshield wipers would clear. They just spray matt clear onto the rest of the glass. It will give it a look of dirt but not a huge amount.
If going with the “wiper arc” mentioned, remember that most military vehicles of the time did not have windshield washers in them. The only way to clean the window was by hand. The wipers would just smear the dirt / must around, not leave a clean wiper shaped cresent as is so popular on models.