Where does “tamago” come from?

tamago (English) comes from Japanese 卵, from Japanese 子, from Japanese 鼠, from Japanese nezumi.

Ancestry of “tamago”, step by step

Step	Language	Word	Meaning
1	Japanese	卵	an egg, including fish roe; the beginning or...
2	Japanese	子	a child; a girl, especially a dear or desired...
3	Japanese	鼠	a mouse or a rat; general term for members of...
4	Japanese	nezumi	—