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I have been thinking about getting a twin cam 88 harley to go with the Goose. The 96 is also a twin cam. One problem that comes up each time and must be addressed and that is the wearing out of the cam chain tensioners. There are a lot of utube videos on this. I bring this up because if the bike has over 5,000 miles, it would be a wise precaution to check these. If they are worn and are putting the bike out of timing, it could lead to that issue, maybe. I am not a mechanic or diagnostician, but from the little I know about timing, it could be worth exploring those videos. I would be interested in your findings if you want to report back after solving this.
I have owned many Harleys from this era. This is more than likely a Crank Position Sensor problem.I have had many go bad that had the same symptoms as you. Harley codes are easy to pull, no special equipment.Good luck!