I havent tried this, but for some reason, this idea just popped into my mind as I read this. What if you took a pencil eraser, cut it down to the right width for aircraft tires, and put a little paint on the end of it? Then, you could do with the eraser what real aircraft tires would do during landing--they hit the deck, leaving an abrupt starting point to the marks, then they trail off as the plane slows. I would try this on a scrap piece of something first, obviously. Remember a couple of things too, when doing this--landing planes would commonly bounce a bit on their landing gear, so the marks would be short. Also, the landing speeds were pretty slow, so you will want to do this lightly. Also, because of the bouncing, it would be more realistic, I think, to have uneven lines--a plane might bounce on the left MLG first, leaving a heavier mark on that side or even no mark on the other side. And the lines do not have to be straight as an arrow, since uneven bouncing could cause a bit of a curve in the landing path.
If you try this, please do post pics of it.....would like to see if it works.