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My school has all non-competitive secondary journals. If you do a source-cite you are on the masthead for that issue. I did the source-cite in the fall, but the spring one conflicted with a job interview, so I missed it (and didn't get the SA). I plan to do the source-cite next fall. Should I have the journal on my resume at all, and if so, should I mention the gap, or just put it as an activity without a date like my other LS activities?

yes, you should leave it on, and just add the dates you did it (e.g. Fall 2016, Fall 2017)--no need to highlight the gap.

No idea why you wouldn't list without the dates.