The question that I have for you, is how electronically inclined are you??
I had this issue on my '94 Ultra, my neighbor on his '96... I traced it down to a drop in the engagement wire from the bars to the starter.. (Starter V should have been = to Batt V; it was 7v, not 12v!) That wasn't enought to engage the starter. This is why the Cap button (prior to me) works so well! I fixed it in a different way!
I took a relay, and captured the starting button to the coil; then to ground.. The switched side I went from Batt -> relay common, and partial to starter engagement. Using the pin numbers it went somethign like this
Relay (12V/Common)
Pin. Wire
---------------------------------
85 Starter button from Bars
86 Ground
30 12V (Batt)
87 Starter engagement
This has saved my butt since I installed it; that is after I rebuilt the old starter, and then replaced it and 2 batteries. This has been on the bike for about 6 years, never had an issue since!
I'll take pics when I get home of the install! Feel free to PM me with questions!
-G