I think I understand what you want. I have not had much success in passing option arguments for RasterizeLayer (e.g. options=['INVERSE=TRUE']). So I will propose an alternative. I have written the full code to give you perspective. I hope it helps.
from osgeo import gdal, osr, ogr
StructRas = 'E:/Path/to/your/Raster.tif' # Raster on which I will base the structure of the rasterized output (cell size, projection and extent)
OutRas = 'E:/Path/to/your/OutRaster.tif' # Output Raster (will contain the rasterized vectors)
Shapefile = 'E:/Path/to/your/shapefile/ToRasterize.shp' # vector file to be rasterized
UniqueNumerical = 'RstrField' # OPTIONAL if you have a field in the vector layer you want to base the rasterazation on (instead of burning values)
# This needs to be the name of field column in the vector layer and it needs to be numerical
# Getting Vital signs from your structure raster
StructRas = gdal.Open(StructRas)
rasXsize = StructRas.RasterXSize
rasYsize = StructRas.RasterYSize
gt = StructRas.GetGeoTransform()
prjWKT = StructRas.GetProjection()
nowBand = StructRas.GetRasterBand(1)
NDvaule = StructRas.GetNoDataValue() # In your case the NoData value is -9999
# Opening the vector file
inVect = ogr.Open(Shapefile)
inLyr = inVect.GetLayer()
#Creating empty output raster in memory
RasterizedRas = gdal.GetDriverByName('MEM').Create('memory_raster', rasXsize, rasYsize,1 ,gdal.GDT_Float32)
RasterizedRas.SetGeoTransform(gt)
RasterizedRas.SetProjection(prjWKT)
inBand = RasterizedRas.GetRasterBand(1)
inBand.SetNoDataValue(NDvaule) # In your case -9999
inBand.Fill(NDvaule) # In your case -9999
# Use this is you want to rasterize with the values from your specified column "UniqueNumerical" - DO NOT USE BOTH RasterizeLayer's, choose 1
gdal.RasterizeLayer(RasterizedRas, [1], inLyr, options = ['ATTRIBUTE=%s' % UniqueNumerical])
# Use this if you want to burn in values (I have made the burn value 1) - - DO NOT USE BOTH RasterizeLayer's, choose 1
gdal.RasterizeLayer(RasterizedRas, [1], inLyr ,burn_values=[1])
# Writing out the final output raster
gdal.GetDriverByName('GTiff').CreateCopy(OutRas, RasterizedRas)
print('Done')