This is a very interestin thread to me. I am right handed but I have to shoot left handed due to blindness in my right eye. I can see a few fuzzy lights or shadows out of the right so when I'm shooting I close the right eye. For me it is like turning the radio volume down so you can hear someone talking. It's a train of thought thing. Everyone always told me to shoot with both eyes open but it didn't work for me. My suggestion is to try different ways and see what works for you.

Would it be bad to close my right eye but have the gun in my right hand? I mostly been closing my dominate left and shooting with my right hand. I'm kind of new to the pistol that is why I ask to get on the right track and not have to break bad habits down the road.

That's exactly the way I do it and it works great. I'm sure it's not the textbook way, and probably wouldn't work for a lot of people but it's worth a try. After all , the essence of accuracy is repeatability and if you practice what works for YOU to the point it is second nature you are there.
This is going to draw fire so I'll add this:
Only practice what works. Don't reinforce bad habits.