I think in this instance the surnames Eckel and Eccles are probably unconnected. My grandfather was an Eccles who farmed in Ayrshire (one of a family of 11 so there are quite a few around).
The furthest back I have been able to get is to Alexander Eccles who married Marion McIlmorrow at Daltnagan Farm, Barrhill in 1755. They had three children I know of: Alexander, Gilbert and Margaret. Gilbert's son Alexander, who farmed Laigh Corton, was buried in Old Alloway kirkyard near the grave of Robert Burns father, William Burness.
Mungo Eccles was an Maybole Covenanter, but I haven't been able to connect him to my ancestors.
As far as I'm aware, there is no German connection to these Eccles.