I'd suspect a switch on the handle release relay with blue/yellow wire 23-1 on the middle blade is not connecting well to blue/red wire 21-1 when the handle release relay is untripped (handle is locked).
another symptom of this switch not working would be the line unit would not reset when the coin switch is pushed down.
(The line unit will increment the coins played go from 1 to 3 coins played , but will not decrement after it has 3 coin lights lit)
decrement implies it steps down on ratchet tooth at a time. The line unit steps up one tooth each for the second and third coin played, but it reset all the way on the first coin played (if the previous spin was 2+ coins played ... if the previous spin was 1 coin played, the reset coil is not fired because the unit is already reset).
below is the circuit. This is kinda a description of what it's doing:
1] after a spin, the coin switch connects the green highlight to the blue highlight. Blue goes off and powers the payout circuits.
2] when you push the coin switch down, green highlight connects to orange highlight. All the switches in the orange highlight should be closed if you played 2+ coins, so the coin relay, line unit reset relay and line unit reset coil should all power.
if you hold the coin switch down, not much else will happen. The line unit reset relay will stay powered, but the coin relay and line unit reset coil will unpower by themselves assuming the wipers reset on the line unit correctly.
3] when you release the coin switch, green is connected to blue again and in a circuit not shown the handle release relay should trip to unlock the handle.
4] if you push down the coin switch again, the handle switch in the orange highlight connects to purple and the line unit step-up relay powers instead to move the lights and payout to 2 coin play.
suggest after a spin you:
1] find blue/yellow wire (23-1) on the handle release relay switch.
2] connect one end of a jumper to it, and touch the other end of the jumper to yellow wire 30 on the coin switch.
3] I'm guessing nothing will happen.
4] move the jumper from 23-1 to blue/red wire 21-1 on the mating blade on the handle release relay and touch the other end of jumper to 30
if the coin relay trips, your problem is the handle release relay switch your jumper is on isn't working even if it looks closed.
if jumping 30 to 21-1 doesn't do anything, you may have a "reel 1 snap switch" in the circuit (second pic). That would be a microswitch sitting on top of the slotted metal plate the reel wipers arms are moving in and the switch changes state when the arm is pulled back as the handle is pulled down.
the snap switch appeared on later 831 games ... yell if you have it.
note while it's possible you have multiple issues like the coin relay switch AND the line unit open at '0' switch in the orange highlight don't work AND there's a plug connection/coil issue with the line unit reset relay, it's not likely all three of those are bad at the same time.
if the handle release relay and coin relay are both reset/latched and pushing down the coin switch does not trip the coin relay but does reset the line unit, then it would be one of ... : (Are the Coin Relay switch & Handle switch open or closed when they are reset/latched? )
the metal armature plate is away from the coil top when those relays are reset/latched. However, they are trip relays, so when the coil powers and the armature plate is pulled onto the coil top, a switch on the relay disconnects the coil power. The armature plate can move away from the coil top a little, but the relay is still "tripped".
when the relay is tripped, the switches should all have changed state from what they were doing in the latched/reset position.
Could it be something in the Line Unit?
nope. The only thing an open "zero position" switch on the line unit could do is prevent the line unit from resetting. That switch is poking out over the white plastic ratchet/gear and is open when the unit is reset, closed at step 1+.