I am not seeing evidence of "Ann Cockburn" as daughter of Sir William Cockburn of Langton, 1st Baronet and Lady Helen Elphinstone
The Records of the Cockburn Family by Sir Robert Cockburn (1913) states that " Sir William and Lady Cockburn had four sons and two daughters: William, the heir, created a baronet in 1 627 (of whom hereafter), John, James, and Michael; Isobel and Jean." (page 46). https://archive.org/details/recordsofcockbur00cock/page/46/mode/1up I have detached Ann from William and Helen.
On Wikitree, for Sir Gilbert Eccles of Shannock it is written: "First marriage: Can have occurred around 1630, when Gilbert was still living in Ayrshire. Many historians have suggested his first wife was Anne Cockburn of Langton, but there are no records to prove this." Does anyone have evidence for the name Ann Cockburn which is currently attributed to this profile? https://www.wikitree.com/wiki/Eccles-88