You can get to Goodsprings from Eagle Ranch, but the first mile or so of Eagle Ranch is hill after very steep hill of loose rock. 4Lo can get you up and over, but it can get ugly in some spots. The best route from Blue Diamond to Goodsprings would be the Cottonwood Pass connector which starts from Blue Diamond here:
Just keep following Cottonwood Pass south, without taking any forks, until you reach here:
Town of Goodsprings is just south of there or you can follow the previous coordinates to the camp sites.
If you'd rather find a shower and bed, you should head south to Goodsprings and head East on Goodsprings Rd. toward I-15. The Gold Strike Hotel and Casino is right there at the interstate. Maybe 10 minutes from Goodsprings.
If you want to save some time, you can get to that hotel directly by just heading south on I-15. If it were me, that's what I would do if I wanted a hotel. Just stay at the hotel and get a nice rest that night. Head to Goodsprings early, do your exploring and just start south and work your way north, exiting at Blue Diamond.
It's a nice route I think you might enjoy more.
My meds are kicking in. Goodnight!