Just for the benefit for others who might be experiencing the same C1300 code, I have a bit of an update. As part of the process of swapping out the Skid Control ECU, you are required to perform a Linear Solenoid calibration. I thought I would familiarize myself with the procedure before I did the swap, so did the calibration with the existing ECU. Well, after I did the calibration, the yellow brake (!) light has stayed off. It's been two days and the light has not turned on at all. Prior to the calibration, it stays on more than it stays off. The C1300 DTC can still occur and be stored, but it doesn't turn on the brake light anymore. The re-calibration appears to have done enough to turn off the light, but not enough to turn off the DTC. I am going to leave it for a week to see if the light comes on at all, but since I already have the replacement ECU, I plan on swapping out the ECU next week, just to get rid of that C1300 DTC.
After the calibration, the light pretty much stayed off for months, but last week, it came back on and I finally swapped out the ECU. For those so inclined to swap it out yourself, there is no need to drop or remove the steering column. The bottom two bolts are easily accessible but the top bolt is difficult. In the end, I managed to get to it with a long set of wobble extensions shafts, from the front of the dashboard. You do have to pop out the side vents and the panel above the steering column, but that is a whole lot easier than removing or dropping the steering column.
After the swap and re-cal, all trouble codes are clear and the light is off. Hopefully, that's the end of that!