You can put a meter (ohms/continuity range) on the terminals & see if it switches properly.
If you haven't a wiring diagram, here's one att. (Reccommend getting at least a Haynes manual if you intend to keep the bike any length of time.)
Besides needing clutch in or neutral to enable the ground side of the starter relay (solenoid), the Igniter must get a ground input, in order to run, on one of the grey/white or green/white wires which are from the clutch/neutral combination & sidestand switches. Note, the grey/white also loops thru' the factory option alarm, if fitted.
98 Tbird tank/seat, Sprint fairing, ZX7R forks+Racetech Gold Valves, 08 ZX6R shock, Alcon 6-pot, Ignitech+TPS, T'bike 3-1+Beowolf can, airbox mods/rejet, tubeless wheels, lots :) per mile.