Hold Light, Transmission, and Tune-Up question about a problem

I have had my 2006 Aveo since 24,000 miles. It now has 81,000 on it about 6 years later. I have used these forums through the years to fix issues here and there and I want to thank everyone for all the help on here (I finally just signed up). I will discuss my common issues as I think they may be related. The problem is that since day one of owning it, I have had issues where the car has trouble idling at first in the morning while warming up. It also can die while driving slow, slowing down, or sitting at a stop. Finally, the biggest problem is that the hold light will come on flashing here and there, sometimes seemingly from nothing, and other times it occurs after the car jerks weirdly. The jerking is while driving the car will act for a second like I slammed on the brakes and then keep going, as if the transmission had an issue. Then I'll have to drive for a day or two with the 3 gears until the hold light is off, then it will just not occur anymore.

The problem with all of these symptoms is that none of them are systematic. They occur extremely randomly, and sometimes will not occur for months at a time. The other confusing issue is that the car has done this since I purchased it and it still runs great aside from these issues. Over the years I have taken great care of the car, oil changes and all. It had the thermostat replaced, and I replaced the housing with a metal one. I have had the transmission fluid flushed every other year, and I have had the cooling and oil flushed before. I just (yesterday) changed the timing belt, water pump & o-ring, serpentine belt, valve cover gasket, spark plug wires, and spark plugs (iridium, not platinum). Also, I was told by a lifetime mechanic that my cams looked great (while the valve cover was off) and indicated that all my oil changes had been good. Even at 81,000 miles, the original timing belt also looked great. The hold light and jerking issue is still occurring and the car still died this morning while on idle.

I am hoping some more advanced owners here may be able to enlighten me on some of what I described here, because I have not been able to find specific help on some of this, and I feel I have tried a great deal to take care of this car and even put good new tune-up pieces on it at regular intervals, yet it still gives me some of these problems. Thank you again for all the help I have found on these forums, and thank you ahead for your help, I am simply trying to include all the description I can so the situation is clear to any who may be able to help me find ways to approach this further without randomly pouring money into the car.

Have you checked to see if any OBD codes were set? Can you correlate these problems to wet conditions (rain/snow)? Being so erratic, it sounds electrical. But the problem is there are a bunch of usual suspects - coil pack, crank/cam position sensor, exposed/lose/cracked wire(s), TPS. But there are other possibilities as well, and hanging parts starts to get expensive fast. Plus, it's also possible the problem is fuel-related (pump, filter, injector). Best to diagnose, but that requires some know-how, and a probably a good manual. If you haven't done so already, check to see if a code was set, which might point to the exact problem. The erratic ones can be a real PITA :(