The neutral switch most likely got stuck in the 'open' mode, due to being compressed by the shifting mechanism for an extended period of time.
I'd check the sockets for the turn directionals, if it's dirty ( corrosion, etc.), check the center contact, and see if it has been pushed down by being in contact with the base of the bulb.
Also check the bottom contact of the bulb, and see if the lead contact point where the spring tab on the socket contacts it, for a divot in the metal, or a general deformation of the area.
The turn directional switches do fail, I'm on my second replacement switch.
These bikes on average are 25 + years old, and things do go bad with age, not just usage.
I like to add this tidbit of information on lightbulbs, it was not in an automotive application, but still interesting none the less.
I had a 100w halogen light bulb in a kitchen, overhead light, it started going on and off, plus just flickering for an extended period of time.
I removed the bulb from that socket, and installed it in a table top lamp, and it worked fine for the time I had it in there.
Reinstalled the halogen bulb back in the original fixture, and sure enough it started 'acting up' again.
I spent many hours checking out the wiring in the house, it was a new construction home, so anything was possible.
Turned out to be a bad light bulb !!
I had a 'trouble light' that used an incandescent bulb, so I installed the halogen bulb , and when I rotated the light to where the bulb was pointed down, it became intermittent, when it was rotated 180 degrees, the bulb worked fine.