Yep, it depends on how much time you plan to take off though and of course how much you make. If you wanted to take a year off, for example, then you would be wisest to work through June, then start in July of the following year since individual income taxes are progressive based on the calendar year. If you take off a shorter period, then you might take off November through February. I run these numbers through the SmartAsset tax calculator to get an idea of the effect on tax.
I don't think timing matters with regards to health insurance unless you're going to have some unique medical expenses. If you can find out how much your employer contributes to you medical premiums, you can then compare costs for COBRA vs. switching to an ACA plan. Also if you're taking off to do international travel, I would definitely consider an expat plan -- much better deal than US plans.