How can I get around a large gap in my employment history on my resume? I took some time off to take care of my elderly parents but do not want this to reflect poorly in the eyes of a future construction employer.

I can guarantee you that during an interview any history gap will be questioned. But, your goal is to make it to that first interview.
Gaps in employment history send up red flags. Employers wonder if the construction executive job seeker could have been imprisoned, on disability, in a psychiatric ward or worse. The best thing to do is explain.
For example, if you took some time off for personal reasons such as to be with your elderly parents until plans could be made for their well-being- write this in your cover letter. Stress that this situation is behind you and you are eager and ready to begin again. Most employers will admire your honesty and readiness to move forward.