I have got an idea!!!
I thought of an idea (and tested it) to make it appear nearly instantly. Firstly, I buy some repels. (1 or 2 is enough) Secondly, since usually an Eevees' level is 18-19, I get a Pokemon level 18-19, also, to be the first in my party. Then, I use the repel and walk/run around in the grass until it appears. A little fact, though, in case you're a bit skeptical: Eevee is the only Pokemon in that area that is level 18-19 that you will run into without having to walk into rustling grass. I did this and in the next 5 minutes, I had already run into 4 Eevees. If you don't believe me, just test it out and you'll see. :3
Hope this helps!!