Pz IV H production and zimmerit application has many variations. Some Pz IV H’s (production start April 1943) didn’t have zimmerit as Zimmerit appears in ~August 1943. The three Pz IV manufacturers (Vomag, Krupp & Nibelungen) have some variations in what was applied even with the vehicles they produced.
This thread discusses some of those variations.
missinglynx: nibelungen-panzer-iv-h-initial-1944-zimmerit
This golden oldie provided a concise overview of German WW2 afv’s:
For discussion only, here’s a snippet for the Pz IV H. My understanding is most of the equipment in Normandy was newer so I believe the vast majority of Pz IV H’s would have zimmerit at that time.
Craig Ellis wrote several Pz IV books that delve into specifics of the manufacturers. Apologies but I’m not enough of an aficionado to accurately summarize the specifics.
Regarding zimmerit application, here’s my favorite way to do 1/35 scale. For a 1/25 scale Panther (long ago), I used part of a razor saw blade & spackle paste. I think with the right blade it would work for 1/12 scale.
HTH