What alarm is it????? Is it the Triumph/Datatool alarm or some other make???
I ask because I've been in touch with Triumph about the problems I had with mine....
I had the alarm fitted because I was under 30 and it took £150 of my insurance quote. I was still paying over £400.... The alarm has paid itself for this year! Also I don't have a garage, and it's parked in a public car park at work. And it was fitted between failing my first test and passing my second....

:
Anyway I digress...
My receipt says genuine Triumph Alarm....but it wasn't. I'm now on alarm number 4 that is a genuine Triumph alarm....
With the geniune alarm, it should plug straight in. They put a plug in the harness so there should be no hacking into the cables. With the one I had fitted they had to cut into it. With modern bikes having a processor thing they'll be as prone to problems with static as a computer. And static can go through a system like a dose of salts.
So if your alarm is not Triumph/Datatool....
See what I mean???
Get the coils changed. I'm not a technical person, but your problems sound the same... though I don't have a tacho, so that bit I don't know about.
If that doesn't help, then get in touch with Triumph. At least you'll have done all the sensible stuff before ranting at them...