In a species of insect, the gene for body colour (alleles $B$ for grey, $b$ for black) and wing shape (alleles $V$ for normal, $v$ for vestigial) are autosomally linked. A homozygous dominant insect with a grey body and normal wings ($BBVV$) is crossed with a double mutant insect with a black body and vestigial wings ($bbvv$) to produce the $F_1$ generation.

An $F_1$ dihybrid female is then backcrossed with a double mutant male in a test cross ($BbVv\times bbvv$). The arrangement of the genes on the homologous chromosomes of the $F_1$ female is shown in the diagram below.

Given that the distance between the two gene loci is $12cM$ (centimorgans), what is the expected percentage of the test cross offspring that will display a grey body and vestigial wings?