Great question. There are two different structures here so let's look at each. First, you say that the "customer's home" is not in a (high-risk) flood zone. Therefore, flood insurance is not required on this structure.
Next, we have a mobile home that is located in a high-risk flood zone, but is not taken as collateral. If the structure (i.e. mobile home) is not taken as collateral, you do not need to get flood insurance on your loan. That said, you will want to ensure that the mobile home is titled (and you aren't taking the title as collateral) - otherwise, if the title has been surrendered, it actually becomes part of the real property, meaning that it technically would become collateral requiring flood insurance.
So to answer your question, no, you do not need to require flood insurance due to flood insurance rules. Requiring it as a Safety and Soundness concern, however, is another question.
_________________________
Adam Witmer, CRCM
All statements are my opinion, not those of my employer, and should not be taken as legal advice.
www.compliancecohort.com