About this detail of the Tiger
In Spring 1944, S.Pz.Jg.Abt. 653 requested ([3] page 371) one or more Pz.Bf.Wg. (command vehicles) of the type VK4501 Tiger (P). This type of tank had been designed in 1941 and some were assembled before cancellation of the project in October 1942. The tanks were never used in combat, but the hulls were used as the basis of the Ferdinand (later Elefant) self-propelled gun. Since the unit was outfitted with Elefants, a tank with a similar hull would share components and thus be easier to maintain than a vehicle of a different type.
At least one tank was delivered to the unit. Dragon Models have released a kit representing it (reviewed on PMMS).
I cannot comment on the hull of this special vehicle, but I will discuss the turret, which is similar to a Tiger 1 turret. Most of the Tiger (P) turrets were converted for use in Tiger 1 tanks, but four Tiger (P) were kept in working order for tests at the Nibelungenwerke factory ([1] page 28). Two of the four were command vehicles with extra radio equipment, so the tank (or tanks) obtained by S.Pz.Jg.Abt. 653 are very probably these ones. The presence of a smoke signal basket on the cupola supports this idea ([2] page 6-20).
The first 8 turrets built for Tiger (P) had a low roof made of 3 plates, but the rest had a higher roof made of a single bent plate. The leftover command vehicles carried turrets #13 and #14 and therefore had the high roof. Photos of this special vehicle show a high roof.
The vision ports at the sides of the turret were positioned low down in the first Tiger (P) turrets with the low roof. Later, the vision ports were moved upwards to take advantage of the extra headroom under the high roof. The curious thing about this command vehicle is that it has both the high roof and the low port. If we are looking at turret #13 or #14 from the Tiger (P), then it seems at least 5 Tiger (P) turrets were made in this way, possibly many more. This feature was not associated with the use of these vehicles in the command role, because turrets #13 and #14 were built as normal turrets and converted later for command use [2].
Since most Tiger (P) turrets were converted for Tiger 1, and since you cannot practically move the vision port in a finished turret, we would expect a few turrets on early Tiger 1 tanks to have lower vision ports than normal. But I cannot find any photographs of such tanks.
The above diagram shows the differences between the turrets from the Tiger (P), the first production Tiger 1, and the vehicle obtained by S.Pz.Jg.Abt. 653.
[1] DW to Tiger 1