A business sign may not be eligible on its own, unless it is of some artistic merit. Otherwise, the business may possibly be eligibile, as long as it isn’t a generic business, such as a grocery store.
A health clinic is a little harder to judge, as I don’t know if you are referring to a place where one may go for a medical appointment or to seek medical treatment, or a fitness center/studio, where one can get some exercise. A place you go to get medical treatment is typically seen as a generic business, but there may be other POIs inside that are eligible, such as art.
I would recommend reviewing the Wayspot Criteria, to understand better what may or may not be eligible. You may also want to check out the Criteria Clarification Collection, as it covers some of the most commonly discussed POIs. There are sections there for places like Generic/Non-Generic Businesses that may be helpful.
And yes, don’t assume that since there are Wayspot for certain POIs in-game that they are eligible, as eligibility does change from time to time.