The base spirit of a gin refers to the distillate to which botanicals were added. It’s helpful to think about the base spirit as a vodka-like spirit that the distiller used as a starting point— a blank canvas upon which the gin was designed.
But choice of base alone doesn’t mean that you’ll be able to taste it. Depending on choices the distiller makes, such as how many times the base is distilled, or to what strength it is distilled to— there might be no character at all coming from the base spirit.
Gin is rather unique among spirit categories. While many spirits are defined by the type of distillate— for gin this is not true. Gin can have any base spirit, and as long juniper is predominant. It’s gin.
Grape Base is particularly complicated, because there are great deal of specific categories that refer to different parts/ways that grape is treated during the distillation process. Gins which feature a grape base could fall into any one of these categories.
Grape Pomace (the leftovers of the wine making process) is the process which creates Grappa, Zivania, or Grozdova. Burnt wines— b.k.a. Brandy— use wine as the base. This category also includes Armagnac, Cognac and Pisco. But furthermore, grape alone can be used as a base. This would be something akin to a grape eau-de-vie. Though like any other base, grape can be distilled to a point of nearly pure neutrality leaving absolutely zero grape character.