Short-duration flares at millimeter wavelengths provide unique insights into the strongest magnetic reconnection events in stellar coronae, and combine with longer-term variability to introduce complications to next-generation cosmology surveys. We analyze 5.5 years of JCMT Transient Survey 850 micron submillimeter monitoring observations toward eight Gould Belt star-forming regions to search for evidence of transient events or long-duration variability from faint sources. The eight regions (30 arcmin diameter fields), including ~1200 infrared-selected YSOs, have been observed on average 47 times with integrations of approximately half an hour, or one day total spread over 5.5 years. Within this large data set, only two robust faint source detections are recovered: JW 566 in OMC 2/3 and MGM12 2864 in NGC 2023. JW 566, a Class II TTauri binary system previously identified as an extraordinary submillimeter flare, remains unique, the only clear single-epoch transient detection in this sample with a flare eight times bright than our ~4.5 sigma detection threshold of 55 mJy/beam. The lack of additional recovered flares intermediate between JW 566 and our detection limit is puzzling, if smaller events are more common than larger events. In contrast, the other submillimeter variable identified in our analysis, Source 2864, is highly variable on all observed timescales. Although Source 2864 is occasionally classified as a YSO, the source is most likely a blazar. The degree of variability across the electromagnetic spectrum may be used to aid source classification.