<p>The Thue–Morse sequence, when expressed in terms of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \pm 1 \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, exhibits a striking connection to the binary partition function through their respective generating functions, which are mutual inverses. In this paper, we delve deeper into the interplay between these two combinatorial objects. We investigate the structure of binary partitions in greater detail, focusing on partitions of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( n \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>n</mi> </math></EquationSource> </InlineEquation> into exactly <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(k\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation> parts, as well as those with exactly <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( k \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation> distinct values of the parts. Our analysis uncovers new insights into the relationship between binary partitions and the Thue–Morse sequence, enriching the combinatorial landscape linking these sequences.</p>