I appreciate that our models are VERY different but I had this on my +8 a year or so back. There is a electrical make/break contact on the handbrake lever to activate the light, and the movement of the handbrake lever under heavy braking was just enough to activate the contact and illuminate the warning light.
Access to the area is not easy on a trad Morgan without a hoist so I cleaned up the contacts a little, and tightened the handbrake pivot bolt as best I could from underneath, since when the problem has not returned.
Is this a possible scenario for the MTW?