I’ve come to the conclusion I can’t walk and play at the same time. I either stop walking or stop playing.
I mean, having been in marching band in high school…
When I was in band I could play OR march. During football season I marched (and pretended to play) and the rest of the year I play in concerts. Couldn’t do both at the same time no matter how hard I tried. 
It’s just sort of depressing because I sort of romanticise about wandering around playing my whistle…
Or it could be that trying to walk over uneven ground in the dark playing a jig is a bad idea anyway and it’s my brain’s way of keeping me from breaking my neck…
Yes, correct! However, I was a piper and spent a lot of time walking and playing. When I play whistle, I sometimes find myself pacing through the house.
Maybe you could practice in the house where there should be no surprises. I would avoid the stairs while playing. Good luck. Cheers, Cyril.
Do you have songs that you have internalized? The kind you could play in your sleep? If you have some of them, I bet you could walk around. When you can play a tune without thinking about it at all, you should be able to think of other things instead.
When I was newer at the whistle, it took too much concentration to do both walking and wandering.
It gets a lot easier with practice. Now, it’s not a hassle at all.
It’s not the ‘thinking’ part that throws me, it’s the ‘breathing’. I find myself having a harder time playing while I’m walking because I can’t control the breath as well (and, of course there’s the inevitable dog or cat to step over/around/on). I suppose practice is all there is to do about it, short of having the whistle surgically implanted.
I used to do marching band too, but there was a lot more ‘camouflage’ in the surrounding players. 
Practice by playing “Marches”. “The Song of Chanter” is easy and your steps will keep time. Just a thought!
Hi
I’m sure you’ll get it with practice. I’ve seen young girls many different places in the world who can even chew gum and walk at the same time. Now that’s what I call multitasking!
Regards,
Owen Morgan
Yacht Magic
Anchored in the lagoon, St Maarten
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Or, if all that practicing is too much work, you could just hold still. It is sort of fun to pace around, though.
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Tom