Steve Litt:
...
Busybox doesn't do what I guess you want, for that you just
fire up a process supervisor, there are a few to choose among.
Remember busybox init is just a minimal init, everthing else
is some other programs responsibility. You can think of busybox
init as sysv init but with just one runlevel.

But since you asked:

> 1) Does Busybox init require the daemon to background itself?

No, just place it last in /etc/rcS, and there can only be one
such process.

> 2) Does Busybox init give you a reasonable way to automatically restart the process
> after the process terminates?

You can run it in its own console, and there you can have it to
respawn just like a getty.

> 3) Does Busybox init give you the choice of auto-restart or not for each different
> process? If it does, that's something specifically missing in Runit.

Yes, start the process either in /etc/rcS or in its own
"getty" line.

Regards,
/Karl Hammar