The first thing that I would do on any pre-2008 ST1300 is ask the seller if there have ever been any fault codes and which ones. I would then check for fault codes myself. If there are none, it needs to be ridden with the RPM above 4,000 RPM for several minutes (the longer the better)
AFTER the engine has been fully warmed up. Afterwards, check to see if the FI light came on. Whether it did or not, I would check again for trouble codes and what trouble codes are present if any.
If fault code 25 or 26 is either present or has been in the past, I would walk away from it. The most common cause of this failure is a defective ECM. In many cases it will not be repairable due to the ECM no longer being available from Honda, and no repair facility to date has been able to repair these ECM's. Many, but not all, used ones available for sale have this same defect. Unfortunately nobody can know which ST1300 will be affected by this issue, if it will be affected by this issue, or when. All we know is that it is more prevalent on pre-2008 model years. The specific motorcycle that you are looking at may never fall victim to this issue.
Also unfortunate is that the above defect can easily be hidden by an unscrupulous seller by simply clearing any fault codes. As long as the motorcycle is not ridden with the RPM above 4,000 for at least a couple of minutes, the defect will not recur and the buyer will be none the wiser. Riding at 4,000 RPM for only a few minutes may not cause the defect to recur, sometimes it takes longer before it recurs. Thus the longer the road test the better. Every time that the ignition is turned off the fault code disappears and the FI light will not illuminate until the fault is triggered again.
Many people who have suffered this defect and who have not found a good replacement ECM have chosen to continue riding it as is. The most significant consequences that they report are a minor loss of power and a minor increase in fuel consumption when the FI light is on and the fault code is present. Many people are simply keeping the RPM below 4,000 RPM to avoid triggering the fault code and are just living with it as is.
The below article was not written as or intended to be a pre-purchase check-list however, it will give you an idea of what to look at and what to ask the seller about.
Maintenance Items Needed for a New (old) Bike