I was under the impression Eccleston got the job pretty much just because RTD had worked with him before on Second Coming, liked him, and wanted to work with him again.
Other way round. Eccleston approached RTD about Doctor Who
because he'd enjoyed working on The Second Coming
. RTD had thought that Eccleston was out of the production's league. Ironic, as RTD had already offered the role to Hugh Grant who had turned it down.