The First Dell Mapback
The first "Mapback" was Dell #5, Four Frightened Women, by George Harmon Coxe. Having said that, many collectors own a copy of Dell #4 with a Mapback, The American Gun Mystery, by Ellery Queen.
The answer, of course, is that Dell #4 was originally printed without back cover artwork, but the reissue was. The question (as far as I'm concerned) is WHICH reissue. I'm going to assume (after a bit of research) that it was the first one. In other words, I believe that only the first printings of Dell #4 have the old keyhole back cover, though none of my reference materials actually come out and state that.
The American Gun Mystery was originally printed in February, 1943 with a run of 120,000, and was reissued in July, 1943, with a further run of 26,000. It would be reprinted three more times, in '45, '46, and '47.
Several illustrators drew back cover art for the "Mapbacks," but by far the most prolific was Ruth Belew. William H. Lyles, the Dell bibliographer, credits Ms. Belew with the back cover for the #4 reprint, and while #5 is not credited, it appears to be the same artistic style as many of her other illustrations. Lyles states elsewhere in his works that Belew drew her illustrations and submitted them in "batches of four or five," so it would make sense that a back cover illustration for #5 would be submitted at about the same time as the first reprint for #4.