The reserve lighting unit will automatically turn on the other element in the headlight if one should burn out. Just a safety feature to not leave you without light half way around a dark curve some night. If I recall correctly, it only works once per bulb. If you shut the bike off or move the lo/hi beam selector, the reserve unit does not kick in again.
I looked back and believe you have a 2003 model vn750. (Fillout a signature, and give us a little info about your bike, and what mods, repairs or service you have done. It will help figure out what hasn`t yet been done). You do not have signal light cancellation. That was only on the early bikes for 3 or 4 years, `85 to `87 or `88.
Are you saying the safety switch on the sidestand doesn`t shut the engine off if the stand is down when the tranny is put in gear? I`m not sure what would cause that, unless the little arm that sticks out is broken off or bent ,so as not to touch the sidestand when it is down. It is easier for me to see a faulty switch there not allowing the bike to start. In any case, whatever is wrong with it, spray some WD-40 or the like into it and work the switch lever around to clear and clean any mud and small rocks out.
Check your battery voltage at the posts while the bike is running and see what readings you get when the lights brighten and dim as you describe. It sounds like possible r/r problems, or loose connections or corrosion. Clean all connections with electronic cleaner spray and emery cloth or sandpaper, and seal them with dielectric grease.
Do a search for "reserve lighting unit". There are near 50 threads with a couple of promising looking ones for you near the end of the list. Here is one from the Verses:
I hope something here helps you Find the problem.
Edit: Boy am I ever a slow typer, 6 posts made here since I started. Might be a lot of redundant advice in my post. LOL