There have been anagogical experiments of resumes with a gap and without a gap. The results were that the same resumes that had a gap did not fare as well in screening. A solution to this is to "fill" that gap with listing it as a "sabbatical", caregiver, or projects you might have done. If you put caregiver in and they ask, just say you had to deal with a family situation that has now been resolved. That way, it keeps their mind at ease.

Radio silence is not uncommon as there tends to be many applicants who apply. Employers might want to keep the doors open in case they have a vacancy on short notice and call you later. This disincentives them from telling you that you didn't get the job. It may or may not be due to the gap at all.

When you meant "local", did you mean USA or another country? Other countries may have different resume conventions, so you may want to look into that. For example, in some parts of Asia and Europe, it is not uncommon to attach a headshot in the resume. Certain countries may expect certain personal information as well. In France, it is considered strange to talk about yourself in first person in the cover letter (I'm not sure why, but it is the standard). These practices are the opposite in UK, USA, and Canada.

If you're not getting enough responses or invitations for interviews, you might need to revise your resume and application strategy. If you had interviews but not enough offers, you may need to revise your cover letter. Your cover letter is usually reviewed at the later stages.

Without looking at your resume and based on the post, it may be possible that you need to emphasize the transferrable skills and align yourself more with the job posters to be more compelling. I would not delete your international experience, as that would put you in competition with new grads.