Eichkorn is one of two interim coaches taking to the bench this weekend, after Schalke were rocked by the resignation on health grounds of coach Ralf Rangnick.
And the Schalke caretaker will be hoping to enjoy the same positive start as Rodolfo Cardoso had on Friday night, when he led Hamburg to a 2-1 win over Stuttgart.
Cardoso is currently temporarily in charge of Hamburg after their poor start to the season - they claimed just one point from six matches before Friday night - saw them sack Michael Oenning on Monday.
However, both Eichkorn and Cardoso are short-term appointments as two of Germany's biggest clubs search for a big-name figure to lead them back to glory.
"This has swept the ground from under our feet," admitted Schalke's director of sport Horst Heldt regarding Rangnick in an interview with DPA. "It was not in any way predictable.
"It was a shock that we have first got to let sink in. I am convinced we will then be able to present a solution, but we won't make a knee-jerk reaction.
"We will take things day by day. The new coach has got to fit in with Schalke."
Hamburg have a little more urgency, though, with their chairman Carl-Edgar Jarchow admitting "It will certainly not take us two, three or four weeks.
"We are already testing the market and contacting people."
One club certainly not experiencing a crisis right now are Bayern Munich, who have won their last five games in a row, and they will be aiming to make it six against coach Jupp Heynckes' former club Bayer Leverkusen on Saturday evening.
Borussia Monchengladbach could have stolen top spot from them prior to that game when they face Nurnberg while Werder Bremen, who trail Bayern by two points, are not in action until Sunday when they host Hertha Berlin.
Elsewhere, defending champions Borussia Dortmund will look to arrest a two-game losing streak when they travel to Mainz, who have also lost their last two matches, and 2009 champions Wolfsburg will also be keen to get back to winning ways against Kaiserslautern.
Augsburg have yet to win a game in the top flight and they will be hoping to break that duck against Hannover on Saturday while, finally, Cologne host Hoffenheim on Sunday.
Werder Bremen vs Hertha Berlin