Here is a quote from Achtung Panzer about the Ferdinand and Elephant. Seems not all were upgraded with zimmerit, just most. So there is still the possibility of having a Elephant without zimmerit.

Ferdinand and Soviet infantry, Kursk, July 1943.

In October of 1943, 50 survivors were sent back to the factory for badly needed repairs and pre-planned modernization. Modernization consisted of the installation of a MG34 in the hull, improvement of armor protection, installation of wider tracks and installation of commander’s cupola (developed from that of Stug III Ausf G), which provided improved visibility. Most of the Elephants were partially covered with Zimmerite, an anti-magnetic paste. Modernization was made in February and March of 1944 by Nibelungenwerke in Austria and modified Ferdinands were renamed Elephants. Officially Ferdinands were renamed Elephants in general order dated May 1st of 1944.

After modernization, 48 Elephants were grouped into schwere Heeres Panzerjager Abteilung 653 and part of it was transferred to Italy in late February of 1944. They arrived in Rome by train via Salzburg, Innsbruck, the Brenner Pass , Trento and Florence on February 24th of 1944. They saw combat at Nettuno, Anzio and Cisterna as early as March 1st of 1944. sPzJagAbt 654 was moved to France in late 1943 and rearmed with Jagdpanthers. In April of 1944, part of sPzJagAbt 653 was transferred back to the Eastern Front. In Autumn of 1944, all existing Elephants were grouped into newly created unit - schwere Heeres Panzerjager Kompanie 614, sPzJagAbt 653 was re-equipped with Jagdtigers. sPzJagAbt 614 with some 13-14 vehicles saw service on the Eastern Front as late as early 1945 and eventually all remaining (4?) Elephants saw final service with Kampfgruppe "Ritter" in area of Zossen (south of Berlin) in mid April of 1945. When employed defensively in Italy and Russia, Elephants proved to be formidable opponents. As of January 1st of 1945, there were still 4 Elephants in service of which some took part in the defence of Berlin as part of Kampfgruppe Ritter.