The poet is Ann Gibbon, not Arthur Gibbon:
For years I thought that "A.G." was Elizabeth's husband Arthur Gibbon.
It did seem a little odd that he was in Scotland and his wife was far away, and he was asking her to come. But not impossible. They might have been travelling separately, with him gone to visit his sisters.
But in fact it is now clear the poem is written by Arthur's sister Ann Gibbon.
Ann Gibbon wrote multiple similar poems in 1834 to 1852. She usually signed them "A.G."
The June 1834 poem shows that "A.G." is female. The 1852 poem shows that "A.G." is an elderly female and is not Arthur Gibbon.
Finally, the 1850 poem has a cover letter that shows "A.G." is Ann Gibbon.
The 1849 poem below is written from "Ellangowan", Aberdeen, where Ann lives.
Reading the poem again, it is clear that Arthur is not at Ellangowan. Arthur and Elizabeth are on the Continent. And Ann is asking them to come to Ellangowan to visit her.
My Dear Elizabeth - revolving years
Now let me think, what you have done
Your husband lives, and loves his wife
Now let me thank you for your letter
In simple prose, I shall relate
And now adieu, let Arthur know
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