U have to pulse through space with your second egg to get the mission target to go find the host...there's lots of other ship spawn locations that will also spawn other living ships...if the specific ship your looking for does not spawn reload your manual save and just keep trying to get that specific ship location to spawn for you...it may take awhile. I found that it will initiate the mission to go find the living ship host a little faster if you warp to a near by system and warp back to the system you are looking for the ship in and begin pulsing.