Okay, since my previous post I decided to install two separate 4 pin relays and a separate 6 pin toggle switch to solve my headlight problem. As mentioned before, only the high and low beam lights at my scooter didn't work, all other lights worked.
When I tested the power feed to the high and low beam bulb, I did not get any voltage reading.
I didn't trust the small light switch and thin wiring, so I decided rather to install thicker wires, two relays, and a good quality toggle switch to get the lights work properly.
The wiring to the park lights was left as is, because it worked, and I already knew that the battery didn't run flat when the park lights was on.
According to some reading the stators on some models had to be upgraded, because the bulbs on those models draw more power than what the stators could handle, so the batteries kept on running flat.
I did not know whether my Agility has an upgraded stator, or whether the battery would run flat when the high / low beam bulb would work - so I decided rather to install a separate/ independent power feed to to high / low beam bulb. Fortunately I've had a couple of 4 pin relays and 6 pin (On /Off /On) toggle switch which were lying around, so I didn't have to buy anything.
For a start - I'm not an auto electrician, but I do know how relays work. So I concocted a plan to do my own DIY modification. There might be a better way to do a modification like this, but I decided to use whatever I've got.
So I used two 4 pin relays - one for high beam, and one for low beam.
By using the 6 pin toggle switch, both the high and low beam functions can be switched off while the park lights are on when the engine is running.
I wanted the high and low beams only to work when the Ignition Switch gets switched on, therefore I decided to use the thick black wire at the original Ignition Switch as power supply to 86 on both relays. These links (86) and 85 (negative / earth) are just an additional "switch part" on the relays. The switch part on relays only draw small current from the Ignition Switch. When 86 and 85 (the switch part on the relays) get activated by means of a separate toggle switch, the bulb (high and low beam) draws a higher current directly from the battery (via a fuse, and terminals 30 and 87 on the relays).
In the end the modification worked exactly as I was hoping for. A modification like this will not be suitable for other kinds of light problems though.
In short , this is a drawing of what I did: