[ChristianK]

Hi Franck, could you please post this other ebay photo you mentioned or send me a PM? Somehow I have missed it.

Some additional thoughts: the location is actually spelled Braunshardt (syllable division between "Brauns" and "hardt". This was an unfinished airfield intended for use by jet fighter units near Darmstadt.
For this reason I also doubt that this Bf109 belonged to I./JG 53, as this unit was never based in this region so late in the war. Instead 160087 was likely attached either to Stab, II. or III./JG 53, which were all stationed in the Darmstadt area during September and October 1944. If you'd ask me, I would go for Stab/JG 53, but as I am not sure whether or how consistently II. and III./JG 53 used the usual Gruppen bars I won't exclude them. In any case, this aircraft likely belonged to a Stabsstaffel or Stabsschwarm.
The date at which this aircraft could have been left at Braunshardt (autumn 1944) also explains why this is an older G-6 example. From different photos we know that JG 53 was pretty well equipped with the latest variants of the Bf 109 when the war ended. So most likely 160087 was left behind when JG 53 left central Germany and headed southwards in October 1944.

Regards,
Christian