Eimer was born in Stäfa. After spending his junior faculty years as prosector at Julius-Maximillian's University in Würzburg, he became in 1875 a professor of zoology and comparative anatomy at the University of Tübingen.
He is credited with popularizing the term orthogenesis (originally introduced by Wilhelm Haacke in 1893) to describe evolution directed in specific pathways due to restrictions in the direction of variation. Though his theories gained popularity in Germany in the 1880s, his work was not widely known in the English-speaking world until 1890 when his work Die Entstehung der Arten auf Grund von Vererben erworbener Eigenschaften nach den Gesetzen organischen Waschsens(1888) was translated by Joseph T. Cunningham as Organic Evolution as the Result of the inheritance of Acquired Characters according to the Laws of Organic Growth. This book was predominantly a Neo-Lamarckian polemic against August Weismann, his compatriot Neo-Darwinian. Eimer's later work, translated as On Orthogenesis, was a more rigidly orthogenetic text, whereas Organic Evolution maintained a plurality of mechanisms for species formation.
The "Eimer's organs" found in members of the mole family, especially in the Star-nosed Mole, are named after him. He described these organs in the European mole in 1871. Eimeria, a genus of parasitic protozoa, was also named after him.
Maria Linden became a precocious female student of Eimer's. Under Eimer's guidance she was awarded a degree and in 1895 she completed her thesis on the evolution of a snail's shell and she was awarded a doctorate in Natural Science. She worked as an assistant to Eimer until 1899.
He also studied the systematics of Papilionidae.Eimer, G. H. T. Die Artbildung und Verwandschaft bei den Schmetterlingen. Eine systematische Darstellung der Abänderungen, Abarten und Arten der Segelfalter-ähnlichen Formen der Gattung Papilio. xii + 243 pp., 4 pls., 23 figs., Gustav Fischer, Jena, 1889 was published posthoumously from 1889.
Eimer died in Tübingen.
- Gaedecke, R. and Groll, E. K. (Hrsg.): Biografien der Entomologen der Welt : Datenbank. Version 4.15 : Senckenberg Deutsches Entomologisches Institut, 2010 
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