Our research concept is this: Instinct is a body of expert knowledge or belief. The research question is how can we discover and represent it? After all, knowledge representation in humans is a well developed field.
So we have begun to explore the ways that this research might be funded. There are a variety of possible funding sources, because animal behavior is also a well developed field. We have done both federally funded and privately funded research in the past and both of these sources are available for animal behavior.
On the US federal side both NIH and NSF have programs related to animal behavior. The focus at NIH is veterinary, which includes instinct driven behavior that is harmful to the animal. At NSF the topic is part of the Biological Integration program. The USDA may do some work in this area as well, but it seems to be confined to agricultural animals.
Private sector research funding comes from a variety of sources. There are foundations that fund animal research, including several for horses. There are also various membership clubs and associations, especially for domestic and sporting animals, including horses.
There are also a number of associations that focus on wildlife and conservation, both of which involve behavior. This sort of research is also done by parks, zoos, conservation preserves, etc. There may be a U.S. Federal research role here as well, because there are a number of conservation and land management agencies.
Another interesting possibility is the emerging practice of "crowdsourcing" or "crowdfunding" where large numbers of people each contribute a small amount to a project. In particular there are a lot of horse owners who are interested in understanding their critters.