I missed open enrollment [the 30-day deadline in the US for new employees to elect health insurance, or else be uninsured for the rest of that calendar year]. It's ultimately on me, since my company did everything well enough by the book. The short version of it all is that they were almost done being bought out when I joined, they changed insurance providers after I signed up for coverage in 2019, I misinterpreted the messages saying "hey, we're changing, the old coverage won't renew next year," and now I'm not insured. Legally speaking, the company has done no wrong, and I need to figure out my next step.

My company has said "the deadline was December 11th" when I asked them about getting insured after the fact now that I know I messed up. They've informed me that the only way I can get coverage is to have a life-changing event, such as moving somewhere that would change my coverage, getting married, having a kid, or starting a new job. 

Right now, starting a new job is the most attainable item on that list. My current role is my first job in software development after about 6 years as a mechanical engineer. I've been in this role for about three months, and unfortunately it looks like I'll need to leave it in order to gain insurance. To that end, I'm going to start interviewing at several new locations. I'm sure they will ask why I wish to leave my current employer, especially after such a short time.

Is the truth the best option here? If I say, "there were some issues during open enrollment, and unfortunately I was not insured once 2020 began. My only real course of action to gain coverage is to change jobs so that I can get something" will that convey a bad message to potential employers, that they shouldn't trust me and that I will drop the ball with important details? Or is this a semi-common reason for people job-hopping as necessary?

Edit: This is only tangentially related to my question, but in case anyone was wondering: I was insured until the end of 2019. Technically, losing your insurance triggers a 60 day special enrollment period afterwards, and after discussing it with my HR, it looks like we'll be able to use this to get me enrolled after all. I feel like the responses below answered my question, but wanted to give (what appears to be) a happy ending to those interested.