Very few of us have ever seen the alternator on a ST 1300. That's probably a good thing, because as Dave D. and SupraSabre noted above, getting at the alternator requires an extraordinary amount of disassembly of the bike... probably more disassembly than any task other than removing the engine from the motorcycle.
If you live up in the snow belt, are retired and have time on your hands, you have a nice warm garage and a full set of tools, and it's January and you are seeking an interesting maintenance task that will keep you occupied for a few weeks... well, in that case, getting at the alternator is the perfect answer to your mid-winter boredom. On the other hand, if it is Friday afternoon before a long weekend in summer, you are just about to leave on a long-planned cross-country tour and your alternator dies, you can kiss those plans for your long-awaited tour goodbye, you ain't going anywhere this summer.
My guess is that it would take a highly skilled technician who has done the job before about one-and-a half to two full working days to re & re the alternator. The process goes more or less like this:
1) Remove most of the front Tupperware, remove the gas tank and air box. Have a new fuel elbow hose on hand for reassembly later ($17).
2) Remove the throttle bodies, in the process, disconnect just about every hose, cable, and electrical connector you see. Remove the rubber mat (heat shield).
3) Remove the front fender and wheel (optional, perhaps, but it sure does make the job a lot easier), remove the radiator and the thermostat.
4) Remove the alternator.
Now, at this point, your motorcycle is seriously disassembled. If you are doing this in January with two feet of snow outside, there are a whole bunch of other preventative maintenance tasks that it makes great sense to carry out at this time, including:
5) Clean out all the crud that has accumulated in the V between the cylinders, and make sure the drain path from the V down to the 'square hole' is unobstructed.
6) At a minimum, tighten all the clamps on the coolant hoses in the V. For greater peace of mind, replace the 2 larger-size hoses on the thermostat (about $30) and the thermostat itself and accompanying O-ring (another $30). Might as well order a new air filter at the same time, since you have it out ($35).
7) Wash out all the bugs & dirt from the radiator, now that it is removed from the moto.
8) Lubricate the throttle cables & front moving parts on the throttle body.
9) Check the valve clearances, because at this level of disassembly, it is really easy to get the valve covers off, and really easy to get access to the right side cam chain tensioner.
10) Remove the galley oil plug (the 'mystery plug') and re-install it, this time with a little bit of gasket sealer around the top flange of the plug.
11) Since the front wheel is off... how are the front brake pads?
Once you have dealt with the alternator (replaced it or repaired it, as the case may be) and begin to re-assemble everything, plan to do a throttle body synchronization before you put the airbox back on the motorcycle. You'll need a manometer to do this.
To successfully complete a major project like this with minimal frustration and maximum satisfaction, there are a few things you will need to have on hand before you start work:
a) a Honda Service Manual for the ST 1300, updated with the latest revisions (see here for the revisions:
Revisions (Error Corrections) to ST 1300 Service Manual). This is essential, if for no other reason than access to the torque values & re-assembly instructions.
b) a torque wrench (essential for this level of disassembly)
c) easy access to your favourite internet parts provider's web diagrams (for example, Partzilla or similar) - this to enable you to see all the various O-rings, gaskets, and crush washers you will need to order ahead of time.
d) a full jug of replacement coolant (available from any Honda automobile dealer)
e) a full bottle of low-strength Loctite for use when reassembling everything.
Below are a couple of pictures that show the alternator in the V of the engine, after all disassembly has been done except for removing the alternator itself.
Michael
Alternator from above
Alternator, viewed from the front looking aft