I bought a domain last night that has a great backlink profile (lots and all relevant).
I have changed the servers to bodis until I have time to work on it and create a site (maybe never, lol).
How long would it take for the backlinks to drop off? It is just when the linking sites notice (maybe never?).
The backlinks won’t immediately drop off because you changed the domain’s servers. It could take quite a while, if ever, for the linking sites to notice the change and update their links. The backlinks should remain in place until the sites actively recheck and remove the dead links.