Did you finally work out the issue as mine does exactly what your car does? Mines a 2009 and I have a Steinbauer CPU unit fitted to my car and Toyota blamed the unit. I’m getting exactly the same code under similar conditions but never happened whilst not towing, only difference is I had a MAF sensor fault as well and changed that out and that fixed that code but now my mechanic is about to change the boost control valve to hopefully fix it.