I have a 2008 ST1300 with 84,000 kays on it, so mine isn't far off that burgandy one. I haven't had to touch anything except the oil plug and rear trans plug. If it starts and runs smoothly and quietly and revs without rattles and fuss the motor is probably sound. There's an on-going discussion on the Forum about possible valve sticking in a younger ST13, but that's far from certain and unheard of in the hundreds of ST13s that have passed through these pages. There's a factory-recommended valve check, I think it's at 120,000 but anyone who has had it done found no requirement for adjustments. Put it on the centre stand and spin the back wheel in neutral to check the drive train for noise- again, not an issue we've heard of. If you can pull the back wheel, check the splines for grease. There are occasional issues mentioned in the Forum regarding the FI light. If the light goes out after a couple of seconds of turning it on, and stays out, it's fine.
The fact is, they are very reliable and if it's going fine, a complete oil and filter change will set it up for many more thousands of kays. Stinky Pete's has just passed 200 thou with no problems, and there are examples in USA exceeding the quarter mill mark.