I did some more research on that timer. I think it will do what you want, but I bet I could have found one that was easier to set up than that one. I finally found the user manual, and I can see where programming it will be tricky. But once you figure it out, it should be fairly straightforward.
The only problem is setting the time delay. You have to basically know how long you want it to stay on before you program it.
I like the simple ones with a knob that you just turn until the wiper runs as long as you like. But, if you time how long it takes the wipers to make the number of passes you want, then you just put that into the timer and it should work.
Basically, you put the little timer into programming mode, and when you get to the timing length, you short a wire to ground for the length of time you want the timer to run, then open it.
The timer remembers how long you did that.
To tell you the truth, you might want to have a cheap momentary switch handy to help with the programming. You have to connect and disconnect a wire to ground for the number of times corresponding to the function number from the manual.
For instance, to program it for an off delay, which is their name for what you want, you will have to pulse the white wire 12 times. If you are just touching the wire to ground that many times, it would be easy to accidentally hit an extra time or miss a time.
Fortunately, if you do select the wrong function, you can go back and overwrite the programming.
Either way, I think you will be surprised by the size of the darn thing. On Amazon, it looked fairly substantial. But from other pictures, it looks like its about the size of a postage stamp.
I think you will get a manual with it, but here is the link to the one online.
http://www.3rdbrakeflasher.com/documentation/Multifunctional_Timer.pdf
Lots of folks say its best to watch some of the yourtube videos also because the manual is supposed to be hard to understand. That may be true, but it made sense to me. Or at least it seemed to.
Of course, I often work with manuals that have been translated from other languages, so that might have helped.
Let me know how the well the timer works or does not work. I am always on the lookout for useful tools to put in my virtual toolbox.