Will A Month Lapse in Coverage Affect Coverage of Preexisting Conditions Moving Forward?

I turned 26 earlier this month (November). I was aware this meant I would be dropping off of my parents’ insurance and would have to go through my own employer to have my own. My employer’s open enrollment starts the first week of December and goes into effect January first. Already have the paperwork all filled out and ready to mail.

This is where things get tricky. I was under the belief my parents’ insurance would have me covered until the end of the year when in actuality it only goes till the end of the month. With it being the last day of the month (November 30th) I don’t see any way around not being covered for December. I can skip routine doctor appointments and should have enough medication to last me the month, but my father is expressing concern that there being any break in coverage could result in the renewed policy having an excuse not to cover “preexisting conditions”.

Can anyone shed some light on this? Is my father correct? Is there more I should be doing? I’m in a little over my head here.