IC9 appears to be an inverting buffer, so it'll be easy to check whether it's the problem, just compare pins 4 and 16 are both high. If IC9-4 is low, however, then you'd have to go back to IC7C and check the two inputs (pins 9+10) of that. If either is low that'll cause the kicker to turn on. 9 should read high unless the sling switch is closed (so always high with 2J13 unplugged), and 10 should read high except during solenoid test when the CPU fires the coil. It could also be a bad pullup at SIP6 leaving the input to pin 9 floating, but that's less likely.