I found a photo on the internet (not mine, I don't know who created it) that illustrates the various controls on the back of the (presumably North American) headlight for the ST 1300.
Controls on ST 1300 Headlight
I can confirm that the identification of two large (light grey) knobs at the lower outboard corners of the headlight is correct, and that the identification of the vertical adjustment for BOTH lights (left and right at the same time) that is called out by a yellow circle is also correct. That bolt-head within the yellow circle can be operated by either a 13 mm socket on a long extension or by a long Phillips screwdriver.
I recommend that you do not remove the rubber cover (sort of a small rubber tit, like you would expect to find on a waterproof toggle switch) that is labelled "Vertical Adjust Screw". First off, it is absolute murder to get that rubber tit re-installed unless you remove an hour's worth of Tupperware. Second, whatever is behind it is recessed far inside the headlight assembly, and it is impossible to either see in there or get a tool in there unless you remove the headlight from the motorcycle (probably a day's work).
I have never fooled around with the two small bolt-heads at the bottom middle (L Vert Adjust & R Vert Adjust), so, I can't say whether those controls work or not. I have never encountered a ST 1300 that has a problem with different vertical alignment between the two headlights that has not been caused by loose or incorrect placement of the bulb in the socket that receives it. If you notice a difference in the vertical height of the light coming from the left and right headlight bulbs, I suggest you first check to make sure that the bulbs are properly seated in their sockets before you fool around with those two bolts.
When I re-aligned my headlights today, I used the following process:
1) Confirm that both headlight bulbs are properly and firmly seated in their sockets. This is especially important if you are using bulb other than the original 45 watt bulb specified for the motorcycle (e.g. you are using a higher wattage H4 bulb, or LED, etc.)
2) Adjust the large grey horizontal adjustment knobs until the flange visible at the bottom of the headlight reflector is parallel with the chrome surface directly forward of it. This is a "rough-in" adjustment, intended to get you to a starting point where both of the movable reflectors (the deeply concave surfaces with the bulb in the middle, visible in the upper half of the picture below) are pointing straight ahead. There is no need to have the bulb illuminated when you do this, you are comparing the flange on the bottom of the movable reflector with the bottom of the chrome surface that stretches across in front of both bulbs (visible in the bottom half of the picture below).
"Roughing-in" Horizontal Alignment
3) Set your electric headlight adjustment dial (to the left of the tachometer, on the dashboard) to the middle position.
4) Ensure that the weight of the contents in your saddlebags roughly matches the weight of what you normally carry in the saddlebags when you are riding. If you carry varying weights of stuff, average out the weights and load the saddlebags up with the mid-point weight.
5) Adjust the rear shock absorber preload adjuster (large black knob on the left side of the motorcycle, just ahead of the left saddlebag) to the normal position you use for 1-up riding.
6) Sit on the motorcycle, with the side-stand and center stand retracted, with as much of your weight as possible on the seat. Balance the motorcycle with the tips of your toes. Have a helper measure and record the height above ground of the headlight where the middle of the three lines on the clear plastic headlight cover meets the side Tupperware - this exactly matches the vertical position of the headlight bulb.
You don't need to worry about the weight of your riding gear & helmet, or how much fuel is in the tank, because this weight is distributed about equally between the front and rear wheels.
Where to measure bulb height above the ground
7) It is assumed that you are on a flat surface (garage floor, etc.) with a wall, inside surface of a garage door, or other object ahead of the motorcycle to enable you to measure the elevation of the headlight beam. A driveway is unsuitable because driveways typically slope away from the home or garage door.
Turn on the headlight, at the low beam setting. While still keeping as much of your weight as possible on the motorcycle seat, have your assistant measure and record how high the 'hot spot' (implies center of illumination from the headlight beam) is off the wall ahead of the motorcycle.
8) Thank your helper, get the two measurements, then dismiss your helper. Put the motorcycle on the center stand, keeping it the same distance from the wall as it was when you did the hot spot measurement.
9) The object is to now adjust the headlight vertical aim, using the 13 mm nut on the back of the headlight assembly, so that the center of the headlight beam (the 'hot spot') falls at an angle between 0.5% and 2.0% below the elevation of the headlight. For example, if your motorcycle was 10 meters away from the wall when you did the measurements, you would want the hot spot on the wall (measured in step 7) to be between 5 cm and 20 cm below the height of the headlight bulb (measured in step 6).
So, do the math and find out what quantity of adjustment is needed. For example, if you were 5 meters away from the wall, your target height for the hot spot would be between 2.5 and 10 cm lower than the bulb height. Let's say you were 5 meters away, but your hot spot was actually 5 cm
above the bulb height. This means you need to lower the hot spot by 7.5 to 15 cm to get it into the target range. Figure out how much you need to lower the hot spot, and write that figure down.
10) With the motorcycle on the center stand, turn on the low beam headlight, go to the wall, put a piece of masking tape on the wall, and mark where the hot spot is. Now make another set of marks showing where the hot spot should be, based on the math you did. It doesn't matter what the 'height from the ground' of these marks are - what matters is the measured difference (the correction you are going to apply) between the actual hot spot (with the moto on the center stand) and where you want the hot spot to be (in this example, between 7.5 and 15 cm lower than the hot spot (with the moto on the center stand) actually is.
11) Get a 13 mm socket, put it on the end of a couple of extension bars (you need about a foot of extension), grab a flashlight, locate the vertical adjustment nut, and adjust the headlight vertical aim as needed. I suggest you target the middle of the desired range (in this example, the range between 7.5 and 15 cm is 7.5 cm, half of that is a wee bit less than 4 cm, so target 7.5 + 4 = 11.5 cm of adjustment. This will put you in the middle of the allowable range of a 0.5% to 2.0% downward angle of light from the headlight.
12) Take the bike out for a ride in a dark area, and see if you are satisfied with the results. You should be able to then fine-tune the downward angle to your personal preference using the electric headlight adjustment knob.
13) If you are using the OEM specification 45 watt H4 headlight bulb, the horizontal beam pattern should be correct if you completed the horizontal adjustment as described in step 2. If you are using a different bulb (especially if you are using LED bulbs), you may have to make adjustments to the horizontal aim to put the 'hot spot' directly ahead of the motorcycle. Keep in mind, though, that it is always fastest, simplest, and easiest to begin your horizontal adjustment from the default 'parallel' position achieved in step 2.
Hope this helps y'all,
Michael
A footnote: Math wizards might (correctly) point out that a very small angular error is introduced when the adjustments are made with the bike on the center stand, after having completed the initial measurements with the bike off the stand and supporting the rider's weight. This is true, but, the error introduced is negligible and easily compensated for - should it even be necessary - with the electric adjustment knob. The main reason for carrying out the adjustments with the bike on the center stand is to avoid the risk of the bike falling over, and to also avoid the risk of the bike owner getting pissed off with his/her helper when the helper can't find the vertical adjustment nut. 
