Final answer:
The Mediterranean thingamabob's pattern of inheritance is one gene pair with codominance, as indicated by the equal expression of both brown and white color in the hairs of the tan offspring and by the phenotypic ratio of their offspring.
Step-by-step explanation:
One gene pair with codominance:
The mode of inheritance for the Mediterranean thingamabob is one gene pair with codominance. This conclusion is drawn from the observation that the tan offspring have coats with individually brown and white hairs, indicating that both the brown and white colors are expressed equally in the heterozygotes.
When these tan offspring are crossed, the resulting offspring are in a ratio of 1 brown: 2 tan: 1 white, confirming the codominant pattern of inheritance. In codominance, unlike incomplete dominance which produces an intermediate phenotype, both traits are fully and simultaneously expressed in the heterozygote. This is different from epistasis where one gene can mask the effect of another gene, and it contrasts with simple dominance where only one allele is expressed in the phenotype of the heterozygote.