If memory serves, the 360 rear lights have a crude multiplug to connect the loom to the clusters, very much like the Fords of the time.
The fault sounds very much like a bad earth on the stop/tail bulb, could just be the bayonet of the bulb is corroded and needs cleaning or the bulbholder itself or if my memory is correct about the multiplug, the contacts in that and on the cluster - clean them with a soft wire brush, emery cloth or similar but not sandpaper. Once clean and normal service is resumed, disconnect the multiplug from the cluster, smear silicone grease on the contacts of both and reconnect with a final test. The silicone grease will exclude more moisture from corroding the contacts again.
