My understanding is that the dominant eye is the one you see better from overall, e.g., if you wear glasses, the eye with the lowest prescription. I do not wear glasses but my left eye is very slightly astigmatic and performs slightly worse at a visual acuity test, therefore I cover my left eye with the eye patch and read using my right (dominant) eye. However, the orthoptist seemed to be open to try to cover the other eye. I will see what she says after I report my progress. Back to which is the dominant eye, I am not 100% if the weaker eye is always the left for right handed people and vice versa, unless you have had an injury or you have a particular condition. In my case, anything left in my body is weaker than its right counterpart.
An observation I privately mentioned to @mike. I use the eye patch at night to read before sleeping. When I turn the light off, I see a shadow in my dominant eye, the one that was uncovered. It feels like my dominant eye is semi-closed. A couple of times I turned the light back on, went to the mirror and, to my surprise, saw that my eyes were both completely open. With the light on, the "shadow effect" was much weaker. I turned the light off again and the shadow was still there. The room never gets completely dark because of the street lights. I covered my left eye with an hand and the outdoor light getting into my right eye was definitely weaker. I did not notice this the first few times, probably because I was using the eye patch only for a few minutes. Now I use it for as long as I want, typically at least 30 minutes, and the shadow effect is recurring. Has anyone experienced the same? I wonder if it is caused by the LED lamps of the ceiling, as I read my Kindle in bed looking up and, although I try to look away from the lights, there is still some line of sight.
Another observation. As said, I do not wear glasses but I was recommended trying to see if my eyestrain diminishes by using 0.5 reading glasses. When I use the eye patch, I need to move my Kindle an inch further away otherwise I see a bit blurry. It took me a while to figure that out, because at the beginning I thought it was due to one eye giving less clarity than two eyes together. It looks like the onset of presbyopia is different using one or both eyes.
I will see what the orthoptist says regarding those two effects and report here.