Haven't had pheasant for 50 years or so, but as I recall, it's dark meat that's rather dry. I remember loving the taste though...
I would cook it like one would rabbit. The differences abound, yet so do the similarities.
Last time I smoked a rabbit, I made coarsely chopped spinach mixed with salt and finely chopped garlic combined in a bowl and let set for an hr or so. Stuff the cavity, apply rub of choice, and wrap in bacon. Pretty sure I smoked it low for a couple hrs before ramping up the temp until crispy bacon. I quartered the rodent, vac sealed it and froze it.
I was lucky to get 1/4 before my son devoured the remaining 3 quarters (and he doesn't like spinach).
I would do pigeon (squab) the same way. The only other 'wild' bird I've eaten is grouse, and it was always stewed. It was ok, but the process left no wild taste, and the mouth feel was no better than stewed beef.
Keep us up to date as this is intriguing.