IMO, the Honda starter switch (button) having a double contact to interrupt the headlights during cranking is poor engineering.
It would have been much simpler, more reliable and less expensive for Honda to have simply grounded the headlight relay winding to the starter cable at the starter solenoid.
I do this for many relay installs. That would have removed one of the most frequent failure points from the ST1100. By "frequent" the term might be referred to as "extremely rare" for other bikes. ST11's are remarkably reliable beasts, IME.