How to apply the Cahn–Ingold–Prelog priority rules to an isotopically-labeled molecule?

Question

Is the following the correct designation (S) for the chiral carbon in a skeletal representation of 1-chloro(3-¹³C)butan-2-amine?

The CIP rules say to go one at a time by each rule until you find an answer:

1a. Higher atomic number.
1b. Go down the chain until a difference is found.
2. Higher atomic mass.

In this case, even though the $\ce{^{13}C}$ is a higher atomic mass than the $\ce{^{12}C}$, the isotope is ignored because rule 1b says to go down the chain to find a difference based on atomic number first, before atomic mass. Am I correct?

I don't have access to the IUPAC book that has all the rules and many examples, so I used Hanson et al. [1] as my source to get my answer.

Reference

1. Hanson, R. M.; Musacchio, S.; Mayfield, J. W.; Vainio, M. J.; Yerin, A.; Redkin, D. Algorithmic Analysis of Cahn–Ingold–Prelog Rules of Stereochemistry: Proposals for Revised Rules and a Guide for Machine Implementation. J. Chem. Inf. Model. 2018, 58 (9), 1755–1765. DOI: 10.1021/acs.jcim.8b00324 (PDF)

Answer 1

IUPAC's Blue Book is referenced in the nomenclature section of the site's resources for learning chemistry, including the free guide, its four page abstract, and Moss' freely available searchable compilation.

In the later, P-92.1.3 is about the sequence rules "... to establish the order of precedence of atoms and groups [to assign CIP labels]" with

P-92.1.3.1

Sequence Rule 1 has two parts:

(a) higher atomic number precedes lower;

(b) a duplicate atom node whose corresponding nonduplicated atom node is the root or is closer to the root ranks higher than a duplicate atom node whose corresponding nonduplicated atom node is farther from the root.

and

P-92.1.3.2 Sequence Rule 2

Higher atomic mass number precedes lower;

See e.g., chapter P-9, page 9. Though there are some additional rules, the second assigns $\ce{^{13}C}$ a higher priority than $\ce{^{12}C}$. Later (P-92.3) this is illustrated further for instance with

When isotopes are present in a molecule, Sequence Rule 1 is first applied ignoring isotopic differences between otherwise identical atoms or groups. When no decision can be reached isotopes are then taken into consideration, arranged in decreasing order of their atomic mass, i.e. $\ce{^3H} > \ce{^2H} > \ce{^1H}$ (or $\ce{H}$) and $\ce{^{81}Br} > \ce{Br} > \ce{^{79}Br}$.

Consequently, the sequence of priorities in your example is $\ce{N} > \ce{^{13}C} > \ce{C} > \ce{H}$ and thus indicative of configuration (R), opposite to your drawing.

P.S.: a non-bonding electron pair is the very lowest priority withing CIP's set of rules, e.g. in chrial sulfoxides.

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In a comment to the question, GabrielAlx reports ChemDraw assigning (S) configuration and (S)-1-chlorobutan-2-amine-3-13C as a chemical name. Sketching the molecule with isotopic labeling on the demo page of Marvin JS however yields (2R)-1-chloro(3-¹³C)butan-2-amine: