My question is how do you address both short term employment and unemployment on a resume that occurred back to back of each other? It seems like it presents a red flag either way. On the one hand, if the short term employment is listed followed by the unemployment period, then it would seem like job hopping. On the other hand, if the short term employment is not listed on the resume, then unemployment period would be longer than it really was, and that does not seem appropriate. What would be the honest, truthful and best way to handle this type of situation on the resume?
Your resume should state the facts of your employment including accurate start and end dates. Focus your cover letter on explaining the gaps, short-term work along with why this isn't going to negatively affect your ability to perform at this job.
If they just go by the numbers, you may not get an interview, but quality writing and communcation are a selling-point by themselves.
The question is how useful is that short-term employment to the current position you are applying? If I'm applying for a Senior Web Developer position, then I'd hardly think putting down that I worked at McDonald's is going to be that relevant to the hiring manager. While there may be a gap, I'd rather address that in the interview and state that I may have taken jobs outside of IT and thus didn't feel they were relevant for this position.
Consider that whatever you put on the resume is fair game to be asked in an interview. If you put down the short-term position, then be prepared to get asked about it. In short-term positions, I'd highly advise having an answer of why was it so short. Were you filling in for someone on a maternity leave? Were you filling in a short-term contract? Be prepared to explain this and why it was short rather than being what others would have thought it would be.