Try this expression in your mapper:
isNaN(Date.parse($.get('exit_date') || '')) ? null : Date.parse($exit_date).toLocaleDateTimeString()
Having not seen your entire input set, I can’t guarantee it will work for every record, but I think it will come very close, if not fully succeed.
The idea of this expression is:
If $exit_date exists and is translatable to dateobject, it will produce a datetime in which the LocaleDateTimeString() will result into a valid value; otherwise the result is null.
It is dependent on the expectation that NaN is always the result from Date.parse() for non-parsable parameters.
