If he was in cloud and struggling you'd expect he would have maintained his heading at least
No way. If he was IMC (cloud or reduced visibility with no visible horizon), then within seconds his heading would be all over the place and soon after he would be in serious trouble. If the aircraft did not have an AH and only a Turn and bank Indicator, then even the most experienced instrument rated pilot wouldn't last long in cloud unless he was in current practice at limited panel I/F.
Very few instrument rated pilots operating light general aviation twins ever bother to hop into a synthetic trainer and practice instrument approaches with the AH inoperative. Many cannot be bothered to practice limited panel manoeuvers in a ground trainer, either because of the perceived cost of hiring the machine or most probably because they know they will make a fool of themselves and crash. Head in the sand syndrome.