Another possibility with Tamiya's Panzer IVJ , the camou is right, but incorrect theater?
The zero in 806 indicates this a HQ vehicle of the 8th company. I've looked at the three main German tank divisions present at Normandy during June: (12SS Hj, 21st Panzer and Panzer Lehr Div.).
The SS unit has in it's roster only 804 and 805 listed, so that might take it out of the equation.
SS numbering system
Also found a photo of 805, but must be regular Wehrmacht unit as the crew do not have sleeve eagles. http://www.armourworkshop.ca/viewtopic.php?p=1839
Interestingly, Bison decals has a Panzer IVj set,
http://www.perthmilitarymodelling.com/reviews/48/bison/bd48002.htm
and one of the subjects have a white 809, but is of the 12 Pz.Div. eastern front. One picture found of 806, and it has been identified with the same 12 Pz.Div. located in Lithuania.
www.network54.com/...
As for stand alone brown camou, note the Bison set linked above, those of the Normandy examples all have green included. I believe this in keeping with the region we are dealing with, so here is one more final link, monthly average temperatures in the area of Caen (give or take a few degrees if you're into the global warming stuff):
http://www.holiday-weather.com/caen/averages/
regards,
Jack