That is from

dragon.sleepdeprived.ca/songbook/songs8/S8_35.htm

However, many other sites are showing it as is your line two.


From another site, the stanza seems to be coupled with "I see the moon and the moon sees me". It is treated as stanza two of the song:

September 06, 2004 09:21 PM:

My favorite quiet time campfire song:

I see the moon and the moon sees me,
The moon sees somebody I'd like to see.
So God bless the moon and God bless me,
And God bless the somebody I'd like to see.

Now run along home and jump into bed,
Say your prayers and cover your head.
The very same thing I say unto you,
You dream of me, I'll have sweet dreams of you.