First things first, you must dilute the Eyebright prior to putting into eyes; water the best choice. Staying strictly with the Christopher / Schulze approach, both would recommend you dilute with "clean" or "pure" water. In practical terms, distilled is just about the most readily available pure/clean water. I use a common counter-top 1gallon distiller to make my own.
I've used the Eyebright for an eyewash for several years and have used a solid pyrex eyecup that holds about 1/4 to 1/2 ounce of water, to which I add anywhere from one to three or four drops of Eyebright tincture .... your mileage will vary but given the Cayenne in the tincture, it will probably take you a while to slowly work up to how many drops your eyes will tolerate; stinging but a good stinging that will help cleanse tear ducts and part of the sinuses.. An extra step, not required; I put a glass of distilled water and the eyecup in a pyrex pot and lightly boil for a few minutes, cool, fill the eyecup, add a few drops, wash the eye, empty/rinse the cup, refil and repeat for the other eye.
The cautions you've read about " .... sucking minerals out of eyes ... " may be more scare tactics or urban myth and less sound advice. Good luck.