Which eye?

I'm left eye dominant, but right handed. I can't keep both eyes open when I "shoot" images as my rightthumb knuckle ends up in my right eye

I try to shoot (archery) with both eyes open but sometimes I have a strange effect which I can only describe as my eyes fighting for dominance. It really is weird and on those days my shooting is even worse than normal ( which is saying something! )

Assuming that you grip the bow in your left hand, then you need to use your right eye. Try this:
If you normally wear glasses, make up a translucent lens cover (occluder) from a piece of thin perspex moulded to fit over the spectacle frame and then scrubbed into opaqueness with sandpaper. A piece of bubble pack taped over the lens would do for a test.
If you don't wear glasses, get a pair of reading glasses with a large lens size. Knock out the right hand lens and scrub the LH lens.
Now you can release the arrow with the hand you have the most control over.
If this works for you, try taking a few shots with the camera and see how it feels.
Geoff

I'm left eye dominant, and use that for the viewfinder. I just tried an imaginary bow and arrow aim and naturally used my right eye to aim. hmmmm

Bet you are right-handed, though.
The hand drawing back the bow-string, and the cheekbone on that side of the head are parts of the aiming system.
A lot of people consider the cheekbone to be part of the aiming system for shotguns as well where you are supposed to keep both eyes open.
Many years ago, I was taught to use a Sterling Sub-Machine Gun like a shotgun (both eyes open and ignore the normal sights), and found it worked quite well in competition
And a new thought for this thread:
If you are long-sighted, do you have trouble using a normal viewfinder? I know of two people who find a compact digital much easier to use because they can hold it at arms length.
Geoff

Since I started this thread, I have tried to change to my right eye on a couple of occasions, but have given up each time.

Recently assigned AF to the back button on the K-x which made using the left eye a little more awkward. Having acquired the K-5 and done the same with AF, this is even more awkward and I think I'll have to try changing to the right eye again

I am right handed and right eyed.

I play snooker/pool left handed.

left eye right handed play golf and cricket left handed snooker and pool right handed paddle kayak right handed roll left hand side its just to confusing!!

Why are you trying to switch eyes?

So he can watch what's going on with his left eye! Seriously, it can be useful to see what is approaching from out of frame. I'm also left-eyed but right-handed, and I've tried to switch many times but without much luck. I can take a photo with my right eye, but it doesn't feel comfortable.

My dominant eye has change around over the years.
About 20 years ago (with prescription glasses) I found at a fair my shooting was MUCH better with my left eye. (Despite the awkward sighting being right handed)

For most of the last 5 years (without glasses), my right eye was the one for distance views whilst the left worked well for close up. I found with both open I could chose which eye to use depending on what I was viewing. (My options claimed glasses to correct my eyes to work together would have too much difference & give me headaches.)

Now my left eye has been sorted, and is again the better of the two for distance work. Both are now rated at 6/6 (20/20 in Imperial) but the right has slight keratoconus (noticeable only with pinpoint lights - stars etc). Unfortunately for reading both now struggle

but what good is that if you're actually taking the photo under some discomfort by forcing an unnatural viewfinder eye?

I watch what is going on out of frame by periodically looking over the top of the camera with my left eye.

As Tim has said it allows you to follow action coming into frame. If you were focused on a corner in a motorcycle race it helps if you can see the bike as it approaches the coener and about to come into frame. You'll get many more keepers, especially if its doing 170mph. Much more effective than popping your eye over the top of the camera.

The rear focus button on the K=5 is also in a different position than on the K-x. Using my left eye with my thumb on the AF button means I have a choice of either don't put my eye right against the viewfinder, or poke my nose with my thumb, which isn't comfortable

I think this is obviously where personal preferences come into it. When taking pics of thst kind of action ... speedway, stock cars, greyhounds, etc and anything in general where I need to snap quickly I tend to hold the camera just in front of my face and peer over and around the cam. And then quickly go in for the kill so to speak. I'm always aware of goign on around me like that.

This must be differences in face size/shape I guess. Holding my left eye close upto the viewfinder all the buttons to the right of the lCD screen lay to the right of my nose and are readily available under a sweep of my thumb.

Anyway, whatever works for you is the best way.

Very true Smeggy

Yep. I have a pair of sunglasses with card over the left eye for days when it is really bad. Most of the time I can "instruct" my brain a to what to use.
I raise the bow and sight with my left eye closed, when I've sighted with my right, I then open the left eye. It seems to work...most of the time.