Eicholtz was born in Lancaster County, Pennsylvania and graduated from the Moravian Academy of Lititz with a certificate in civil engineering in 1852. Eicholtz was employed by the Pennsylvania Railway from 1852 to 1861, with nearly a year's leave of absence to make a railroad survey in Honduras. Eicholtz served with the U.S. Army from 1861 to 1866, then worked for the Kansas Pacific Railway from 1866 to 1868, which included participation in the 32nd Parallel Survey completed under the command of General William Jackson Palmer. Eicholtz was also employed by the Union Pacific from 1868-1869 and the Denver Pacific and Kansas Pacific in 1869-1870. He was one of the incorporators of the Denver and South Park Railway and served as chief engineer of the line during construction.