Resume Gaps vs. Overlapping Employment: What Do Recruiters Prefer?

What tends to raise more red flags for recruiters: employment gaps or overlapping jobs? I had two software positions simultaneously, and both employers were aware and supportive of this arrangement. However, I lost my main job in August 2023, leaving me with my secondary consulting role, which I’ve held for almost a year now.

While applying for new positions, I haven’t included my consulting job on my resume, resulting in a noticeable gap. Should I list my current consulting role to avoid this gap, or is it better to leave it off even if it means my resume appears incomplete? What do you think would be the best approach?