There are plenty of excellent legitimate reasons for the gap.  So, no decent employer will just discard out a resume. They are trying to find the  person to fill a job.

No, no one should try to cover up something in neither a resume nor an application.
Especially do not omit data in the application. That is a legal document, with a signature bearing to the fact that everything in is is true. If it asks for an employment history and it is left out, it is a form of perjury.

It’s OK to fine tune an individual resume for the specific company or job. But a lie is a lie and there are few excuses for that.

Unemployment happens. Its a part of our modern life.