I am researching George Tee, born 1840 Southampton.
Because of this any reference to a Tee is of interest, hence my response.
The Industrial Revolution occurred in 1830's - 1840's and people immigrated to escape their grim lives in England. Also, the names George and Frederick were very popular (and reoccur through the Tee family tree from UK to New Zealand) The name William crops up in a couple of children born from 1868-1873, in NZ. May be coincidence.
I have picked up on a Army Discharge record for a George Tee (again Southampton, Hampshire, England) which indicates he was born around 1824. It is a long shot, but he may be a sibling of your William. I put in a request for a copy of this record from PRO (Public Records Office, UK) so if you would like a copy I could post it to you.
The other Tee references I have picked up on the web are for a George Tee (born 1845) marrying Lisher Agnes Batchelor 26 Dec1866 at St Mary, Portsea, Hampshire.
There is a John Tee born 1766 marrying Elizabeth Wild 9 May 1787. Hambledon, Hampshire.
Definition of the surname from "Family names in Australia and New Zealand" by Kenneth Allen (1990)
"Tee: L OE 'water, stream' In ME atte ea. 14th century"
OE - Old English (Anglo Saxon)
ME - middle English
If you have a look at a map of Hampshire, you'll find a Tee valley, a river Tee etc.
Debra Jones
Perth, Western Australia