Keith is toking...but heres some more info:
Tach connections:
Red – 12 volt, ties into Neutral light and Oil Pressure light positive. (voltage varies between about 11 and 13 volts DC)
Green/Red – AC voltage and comes directly from pin 15 of the igniter, nothing else on this circuit. (at 1000rpm = @ 6.2, 2000rpm = @ 7.2, 3000rpm = @ 7.5, 4000rpm = @ 7.6).
Brown -ground
Red/Blue – 12 volt, ties into pin 6 (light switch), speedo lights, pin 5 of accessory light connector, then into pin 1 of the ignition switch. (voltage varies between 11 and 13 volts DC).
Purple – not used with tach, clock only.
After looking at the Haynes manual (in color as opposed to the Triumph manual I have in B&W) I am noticing that the Tach is tied into the following via the Red/Blue wire: Light switch, Speedo lights, Acc light connector (pin 5). Got anything tapped in here?
Also, via the Green/Red wire to: Carb Evap system, both carb heaters and both coils. Now that should only be DC voltage which would either make the tach work or not. If there was a bad connection that could make it look like it was jumping.
Does the tach jump between RPM ranges (like if your cruising at 4000rpm…will it jump between 2000 and 4000 or is it more like from 0 to whatever rpm your doing)? If within a range, probably not this circuit. If between 0 and whatever, check it out.
If you test the RED wire you should test it at AC voltage and it should have a consistent increase with RPM. If you can hold it at an RPM level and see it fluctuates significantly then it’s signal from your igniter. Could be caused by a short or a break. If its a short it could be destroying the igniter. If its a break then no big deal. This is only a signal wire to make your tach read voltage.
There’s always the ground circuit again… Maybe there’s a loose ground but I would imagine you would see other signs such as dimming lights and such with items tied into the same circuits. I doubt this but you never know. If the ground was deteriorating maybe theres a wire with a break in it or corroded wires still there.
Theres also the possiblity of the tach being bad. Did Freedom have a Tach on his bike? If the bike gets transported to Spokane maybe you can borrow it to test. Heck if you can get that maybe you can get the igniter too...to test.
adding this for reference: