The Master Surname Index (not online) of the Alberta Genealogical Society lists some 80 Giesbrecht names, among then are;
Peter GIESBRECHT, 1955 - 14 Oct 1972 (son) and
Cornelius GIESBRECHT, 1910 - 14 Oct 1972
both buried next to each other in plot F,05 of the Taber Memorial cemetery. Could these be family of your Peter?? It seems they may have died in some accident on the same day. Could there be a story or obit in a local news paper?
There is also mention of a Peter GIESBRECHT in 2 local history books.
For further research please contact the AGS Research Services Committee of the Edmonton Branch,
http://www.compusmart.ab.ca/abgensocThe Edmonton Branch
http://agsedm.edmonton.ab.caPeter
for the AGS