Geco actually contracted with gun makers for firearms stamped with the Geco logo. Sears contracted with various gun makers in the US in the same way. Sears still does this with their line of tools, as an example, the Craftsman brand dehumidifier I have in my vault is actually made by RCA Whirpool, but it says Craftsman on it and the owners manual says Craftsman. I saw the same machine at Lowes with the Whirpool name. A reprint book by The German Gun Collectors Association states that Geco initially sold ammunition and loading components from 1887 on and began actually manufacturing a line of .22 LF rifles in 1924. These are the only firearms actually manufactured by Geco. They apparently had retail stores in major cities throughout Europe. While no longer still in business as a large retailer of sporting goods, after several mergers, the Geco name is still seen on ammunition made by Dynamit Nobel AG of Austria.
My understanding from a conversation with Dietrich at GGCA is that Sauer and Simson were the largest German makers selling to Geco, but they were the largest German makers period, so that seems reasonable. I am quite sure he said that other makers also provided German made guns, and he pointedly said that the commonly seen Belgian made Geco guns were not of the same quality as the German guns.