Saw the image on reddit and found it very interesting
1. Pick a starting path
2. Pick either the left or the right wall and fill it a different color
3. Follow the colored boundary
This is a much quicker version of locally following the wall on one side of you, and it is still guaranteed to always have a solution no matter which side you pick. To use it, you just have to make sure that the outer boundary of the maze is two separate pieces (in this case, split at the corners). The walls can never connect left to right on the interior or else the maze would be unsolvable, so that is not a problem.
I just found it a very simple yet insightful method.