Sounds like the switch for the left sling is stuck closed, or there's a short in the wiring. Does unplugging 2J13 fix it?

In that case it sounds like an issue with the board itself in the circuitry that fires the solenoid when the pin on 2J13 goes low. If I had the schematics for the RD board I could probably point you to a chip, but I'm not sure if they're available?

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.

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Alright, so it's not IC9. What do you mean about pin 9 reading 'nothing'? It should be high all the time when 2j13 is unplugged due to the pullup. With the game off, can you measure the resistance from pin 9 to 5V/VCC? and compare with the resistance from pin 12? Should both be 4.7kohm

That's... weird. I wouldn't have expected the IC to affect the resistance readings. Maybe it's just a coincidence though... Normally I'd suggest pulling the SIP resistor and checking it out of circuit, but since this is a new board maybe there's some warranty option that would be better?