A while ago, one of my patrons asked me a very good question.
How do priests convince kami to enter, and remain in, the goshintai at a jinja?
This is quite fundamental, but something that I have not seen addressed at all.
In the earliest jinja, the problem does not arise. The belief was that the kami was there already, and the jinja developed in that location as people venerated the kami, and set up a permanent structure for the matsuri. In those cases, the goshintai might be a mountain or waterfall, and the kami is often not clearly distinguished from it.
There are also a number of myths of kami choosing where they want to be enshrined, whether by sending dreams to someone, or by making their will known through fortune-telling. The most famous example of this is Jingū, at Isë, where Amaterasu Ōmikami sent Yamatohimë-no-Mikoto around various locations in central Japan before settling on the current site of Jingū. In this case, the kami has moved, but it was their decision, so, once again, the problem does not arise.
When it comes to people who are venerated as kami after their death, sometimes the veneration happens at their grave, in which case the kami is presumably thought of as attached to the corpse, at least initially. Again, this does not seem to raise the problem. Dazaifu Tenmangū in Kyūshū, which was built over the grave of Sugawara no Michizanë, is probably the most prominent example of this. Incidentally, the other claimant to the title of main jinja for Tenjin, Kitano Tenmangū in Kyoto, was founded through the second method: Tenjin sent people visions about where he wanted to be venerated.
The overwhelming majority of jinja, however, are not like that. People decided that they wanted to venerate a particular kami, and then performed a ceremony to enshrine that kami. There are standard forms for such a matsuri today, with standard norito. While these norito are polite in calling on the kami to come to and remain in this place, they do not envisage the possibility that the kami might say “no”. This has also been common in the past. For example, a lot of jinja enshrining Amaterasu Ōmikami were founded on lands owned by Jingū, so that the kami could watch over them and the local residents could pay their respects. Similarly, in the early Tokugawa period, daimyo across the country were ordered to build jinja enshrining Tokugawa Ieyasu. This does not seem to have involved consultation of the kami. (Tokugawa Ieyasu was already dead at this point.)
These days, it is common for kami to be moved because public construction work is taking over the original site of the jinja, or because one jinja has become non-viable and the kami are to be venerated in another jinja.
I think that the theory has to be that the kami want to move, but that theory does not seem to have any impact on the standard practice. Contemporary Shinto is normally a bit embarrassed about anything that suggests actual messages from the kami, so it is not surprising that the issue is glossed over now, but I am also not aware of anything standard from earlier centuries, when people were much more open about that sort of thing.
One thing that is not involved is some sort of power held by the priests to bind the kami. There are traditions in Japan that have involved that sort of activity, but to the best of my knowledge they have not fed into the Shinto mainstream at any point.
It should not really be surprising that this point is vague, as Shinto does not do precise theology. It just assumes that the kami are still around the jinja, without worrying about how or why.