How could gel electrophoresis be applied to the identification of a gene mutation?

As you are aware, gel uses electricity to separate bands of macromolecular material based on weight. To begin, you would run a control gel. For example, let's say your gene codes for a large macromolecule that barely leaves the well. Next, you would run your mutation; if there is a weight change, particularly around a band related to your gene of interest, such as a protein it codes for, you would say that this was evidence of a difference between samples.

Tl:DR You could notice that your protein—which doesn't have to be protein—is lighter or heavier than usual and use that as evidence that something wasn't right.

Gel electrophoresis can be used to separate DNA fragments based on their size. By comparing the pattern of DNA fragments from individuals with and without the mutation, it's possible to identify differences in the size of DNA fragments, indicating the presence of a gene mutation.