This is a variant or edition of the previous Heins piece, demonstrating the common practice of recycling melodic themes with slight textual alterations. It remains a staple of late-Romantic salon performance.
The student should focus on maintaining expressive control during the slight rhythmic variations from the original version.
Comparable difficulty and character — good candidates for what to learn next.
'Tis not For the Sake of those Beautiful Eyes is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 4.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of 'Tis not For the Sake of those Beautiful Eyes lasts about 3 minutes.
'Tis not For the Sake of those Beautiful Eyes is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include 'Tis not For the Sake of these Beautiful Eyes by C. Heins, Belle of the Ball by Leroy Anderson, Black Beauty by Duke Ellington — see the full similar-pieces list on this page.